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induction, and abduction subsection</span> </button> <ul id="toc-Deduction,_induction,_and_abduction-sublist" class="vector-toc-list"> <li id="toc-Deduction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Deduction"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Deduction</span> </div> </a> <ul id="toc-Deduction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Induction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Induction"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Induction</span> </div> </a> <ul id="toc-Induction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Abduction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Abduction"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Abduction</span> </div> </a> <ul id="toc-Abduction-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Formalizations_of_abduction" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Formalizations_of_abduction"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Formalizations of abduction</span> </div> </a> <button aria-controls="toc-Formalizations_of_abduction-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Formalizations of abduction subsection</span> </button> <ul id="toc-Formalizations_of_abduction-sublist" class="vector-toc-list"> <li id="toc-Logic-based_abduction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Logic-based_abduction"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Logic-based abduction</span> </div> </a> <ul id="toc-Logic-based_abduction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Set-cover_abduction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Set-cover_abduction"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Set-cover abduction</span> </div> </a> <ul id="toc-Set-cover_abduction-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Abductive_validation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Abductive_validation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Abductive validation</span> </div> </a> <ul id="toc-Abductive_validation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Subjective_logic_abduction" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Subjective_logic_abduction"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Subjective logic abduction</span> </div> </a> <ul id="toc-Subjective_logic_abduction-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-History" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#History"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>History</span> </div> </a> <button aria-controls="toc-History-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle History subsection</span> </button> <ul id="toc-History-sublist" class="vector-toc-list"> <li id="toc-Introduction_and_development_by_Peirce" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Introduction_and_development_by_Peirce"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Introduction and development by Peirce</span> </div> </a> <ul id="toc-Introduction_and_development_by_Peirce-sublist" class="vector-toc-list"> <li id="toc-Overview" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Overview"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.1</span> <span>Overview</span> </div> </a> <ul id="toc-Overview-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-The_Natural_Classification_of_Arguments_(1867)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#The_Natural_Classification_of_Arguments_(1867)"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.2</span> <span><i>The Natural Classification of Arguments</i> (1867)</span> </div> </a> <ul id="toc-The_Natural_Classification_of_Arguments_(1867)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Deduction,_Induction,_and_Hypothesis_(1878)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Deduction,_Induction,_and_Hypothesis_(1878)"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.3</span> <span><i>Deduction, Induction, and Hypothesis</i> (1878)</span> </div> </a> <ul id="toc-Deduction,_Induction,_and_Hypothesis_(1878)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-A_Theory_of_Probable_Inference_(1883)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#A_Theory_of_Probable_Inference_(1883)"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.4</span> <span><i>A Theory of Probable Inference</i> (1883)</span> </div> </a> <ul id="toc-A_Theory_of_Probable_Inference_(1883)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Minute_Logic_(1902)_and_after" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Minute_Logic_(1902)_and_after"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.5</span> <span><i>Minute Logic</i> (1902) and after</span> </div> </a> <ul id="toc-Minute_Logic_(1902)_and_after-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pragmatism" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Pragmatism"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.6</span> <span>Pragmatism</span> </div> </a> <ul id="toc-Pragmatism-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Three_levels_of_logic_about_abduction" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Three_levels_of_logic_about_abduction"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.7</span> <span>Three levels of logic about abduction</span> </div> </a> <ul id="toc-Three_levels_of_logic_about_abduction-sublist" class="vector-toc-list"> <li id="toc-Classification_of_signs" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Classification_of_signs"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.7.1</span> <span>Classification of signs</span> </div> </a> <ul id="toc-Classification_of_signs-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Critique_of_arguments" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Critique_of_arguments"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.7.2</span> <span>Critique of arguments</span> </div> </a> <ul id="toc-Critique_of_arguments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Methodology_of_inquiry" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Methodology_of_inquiry"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.7.3</span> <span>Methodology of inquiry</span> </div> </a> <ul id="toc-Methodology_of_inquiry-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Uberty" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Uberty"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1.8</span> <span>Uberty</span> </div> </a> <ul id="toc-Uberty-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Gilbert_Harman_(1965)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Gilbert_Harman_(1965)"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Gilbert Harman (1965)</span> </div> </a> <ul id="toc-Gilbert_Harman_(1965)-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stephen_Jay_Gould_(1995)" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Stephen_Jay_Gould_(1995)"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Stephen Jay Gould (1995)</span> </div> </a> <ul id="toc-Stephen_Jay_Gould_(1995)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Applications" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Applications"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Applications</span> </div> </a> <button aria-controls="toc-Applications-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Applications subsection</span> </button> <ul id="toc-Applications-sublist" class="vector-toc-list"> <li id="toc-Artificial_intelligence" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Artificial_intelligence"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Artificial intelligence</span> </div> </a> <ul id="toc-Artificial_intelligence-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Medicine" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Medicine"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Medicine</span> </div> </a> <ul id="toc-Medicine-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Automated_planning" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Automated_planning"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Automated planning</span> </div> </a> <ul id="toc-Automated_planning-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Intelligence_analysis" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Intelligence_analysis"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Intelligence analysis</span> </div> </a> <ul id="toc-Intelligence_analysis-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Belief_revision" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Belief_revision"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Belief revision</span> </div> </a> <ul id="toc-Belief_revision-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Philosophy_of_science" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Philosophy_of_science"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Philosophy of science</span> </div> </a> <ul id="toc-Philosophy_of_science-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Historical_linguistics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Historical_linguistics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7</span> <span>Historical linguistics</span> </div> </a> <ul id="toc-Historical_linguistics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Applied_linguistics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Applied_linguistics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.8</span> <span>Applied linguistics</span> </div> </a> <ul id="toc-Applied_linguistics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Anthropology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Anthropology"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.9</span> <span>Anthropology</span> </div> </a> <ul id="toc-Anthropology-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Computer_programming" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Computer_programming"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.10</span> <span>Computer programming</span> </div> </a> <ul id="toc-Computer_programming-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#Notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Notes</span> </div> </a> <ul id="toc-Notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Abductive reasoning</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 38 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-38" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">38 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D9%8A%D8%A7%D8%B3_%D8%A7%D8%AD%D8%AA%D9%85%D8%A7%D9%84%D9%8A" title="قياس احتمالي – Arabic" lang="ar" hreflang="ar" data-title="قياس احتمالي" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%85%E0%A6%AA%E0%A6%B8%E0%A6%BE%E0%A6%B0%E0%A6%95_%E0%A6%AF%E0%A7%81%E0%A6%95%E0%A7%8D%E0%A6%A4%E0%A6%BF%E0%A6%AC%E0%A6%BF%E0%A6%A8%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%B8" title="অপসারক যুক্তিবিন্যাস – Bangla" lang="bn" hreflang="bn" data-title="অপসারক যুক্তিবিন্যাস" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D0%B1%D0%B4%D1%83%D0%BA%D1%86%D0%B8%D1%8F" title="Абдукция – Bulgarian" lang="bg" hreflang="bg" data-title="Абдукция" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Raonament_abductiu" title="Raonament abductiu – Catalan" lang="ca" hreflang="ca" data-title="Raonament abductiu" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Abdukce_(odvozen%C3%AD)" title="Abdukce (odvození) – Czech" lang="cs" hreflang="cs" data-title="Abdukce (odvození)" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Abduktion_(metode)" title="Abduktion (metode) – Danish" lang="da" hreflang="da" data-title="Abduktion (metode)" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Abduktion" title="Abduktion – German" lang="de" hreflang="de" data-title="Abduktion" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Abduktsioon" title="Abduktsioon – Estonian" lang="et" hreflang="et" data-title="Abduktsioon" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Razonamiento_abductivo" title="Razonamiento abductivo – Spanish" lang="es" hreflang="es" data-title="Razonamiento abductivo" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D8%B3%D8%AA%D8%AF%D9%84%D8%A7%D9%84_%D8%B1%D8%A8%D8%A7%DB%8C%D8%B4%DB%8C" title="استدلال ربایشی – Persian" lang="fa" hreflang="fa" data-title="استدلال ربایشی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Abduction_(logique)" title="Abduction (logique) – French" lang="fr" hreflang="fr" data-title="Abduction (logique)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ki mw-list-item"><a href="https://ki.wikipedia.org/wiki/R%C5%A9c%C5%A9ra_nyahir%C5%A9kia_(abductive_reasoning)" title="Rũcũra nyahirũkia (abductive reasoning) – Kikuyu" lang="ki" hreflang="ki" data-title="Rũcũra nyahirũkia (abductive reasoning)" data-language-autonym="Gĩkũyũ" data-language-local-name="Kikuyu" class="interlanguage-link-target"><span>Gĩkũyũ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B7%80%EC%B6%94%EB%B2%95" title="귀추법 – Korean" lang="ko" hreflang="ko" data-title="귀추법" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Penalaran_abduktif" title="Penalaran abduktif – Indonesian" lang="id" hreflang="id" data-title="Penalaran abduktif" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Fr%C3%A1lei%C3%B0sla" title="Fráleiðsla – Icelandic" lang="is" hreflang="is" data-title="Fráleiðsla" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Abduzione" title="Abduzione – Italian" lang="it" hreflang="it" data-title="Abduzione" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%91%D7%93%D7%95%D7%A7%D7%A6%D7%99%D7%94" title="אבדוקציה – Hebrew" lang="he" hreflang="he" data-title="אבדוקציה" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D0%B1%D0%B4%D1%83%D0%BA%D1%86%D0%B8%D1%98%D0%B0_(%D0%BB%D0%BE%D0%B3%D0%B8%D0%BA%D0%B0)" title="Абдукција (логика) – Macedonian" lang="mk" hreflang="mk" data-title="Абдукција (логика)" data-language-autonym="Македонски" 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i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Abductive" redirects here. For other uses, see <a href="/wiki/Abduction_(disambiguation)" class="mw-redirect mw-disambig" title="Abduction (disambiguation)">Abduction (disambiguation)</a>.</div> <p class="mw-empty-elt"> </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Mastermind_beispiel_png.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Mastermind_beispiel_png.png/150px-Mastermind_beispiel_png.png" decoding="async" width="150" height="285" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Mastermind_beispiel_png.png/225px-Mastermind_beispiel_png.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a6/Mastermind_beispiel_png.png/300px-Mastermind_beispiel_png.png 2x" data-file-width="404" data-file-height="767" /></a><figcaption>A <a href="/wiki/Mastermind_(board_game)" title="Mastermind (board game)">Mastermind</a> player uses abduction to infer the secret colors <i>(top)</i> from summaries <i>(bottom left)</i> of discrepancies in their guesses <i>(bottom right)</i>.</figcaption></figure> <p><b>Abductive reasoning</b> (also called <b>abduction</b>,<sup id="cite_ref-Josephson_1-0" class="reference"><a href="#cite_note-Josephson-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <b>abductive inference</b>,<sup id="cite_ref-Josephson_1-1" class="reference"><a href="#cite_note-Josephson-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> or <b>retroduction</b><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>) is a form of <a href="/wiki/Logical_inference" class="mw-redirect" title="Logical inference">logical inference</a> that seeks the simplest and most likely conclusion from a set of observations. It was formulated and advanced by American <a href="/wiki/Philosopher" class="mw-redirect" title="Philosopher">philosopher</a> and <a href="/wiki/Logician" class="mw-redirect" title="Logician">logician</a> <a href="/wiki/Charles_Sanders_Peirce" title="Charles Sanders Peirce">Charles Sanders Peirce</a> beginning in the latter half of the 19th century. </p><p>Abductive reasoning, unlike <a href="/wiki/Deductive_reasoning" title="Deductive reasoning">deductive reasoning</a>, yields a plausible conclusion but does not definitively verify it. Abductive conclusions do not eliminate uncertainty or doubt, which is expressed in retreat terms such as "best available" or "most likely". While <a href="/wiki/Inductive_reasoning" title="Inductive reasoning">inductive reasoning</a> draws general conclusions that apply to many situations, abductive conclusions are confined to the particular observations in question. </p><p>In the 1990s, as computing power grew, the fields of law,<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Computer_science" title="Computer science">computer science</a>, and <a href="/wiki/Artificial_intelligence" title="Artificial intelligence">artificial intelligence</a> research<sup id="cite_ref-Josephson,_Magnani_4-0" class="reference"><a href="#cite_note-Josephson,_Magnani-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> spurred renewed interest in the subject of abduction.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Diagnostic <a href="/wiki/Expert_system" title="Expert system">expert systems</a> frequently employ abduction.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Deduction,_induction,_and_abduction"><span id="Deduction.2C_induction.2C_and_abduction"></span>Deduction, induction, and abduction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=1" title="Edit section: Deduction, induction, and abduction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Logical_reasoning" title="Logical reasoning">Logical reasoning</a></div> <div class="mw-heading mw-heading3"><h3 id="Deduction">Deduction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=2" title="Edit section: Deduction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Deductive_reasoning" title="Deductive reasoning">Deductive reasoning</a></div> <p>Deductive reasoning allows deriving <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> from <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> only where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> is a formal <a href="/wiki/Logical_consequence" title="Logical consequence">logical consequence</a> of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span>. In other words, deduction derives the consequences of the assumed. Given the truth of the assumptions, a valid deduction guarantees the truth of the conclusion. For example, given that "Wikis can be edited by anyone" (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bbf42ecda092975c9c69dae84e16182ba5fe2e07" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.284ex; height:2.009ex;" alt="{\displaystyle a_{1}}"></span>) and "Wikipedia is a wiki" (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/270580da7333505d9b73697417d0543c43c98b9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.284ex; height:2.009ex;" alt="{\displaystyle a_{2}}"></span>), it follows that "Wikipedia can be edited by anyone" (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span>). </p> <div class="mw-heading mw-heading3"><h3 id="Induction">Induction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=3" title="Edit section: Induction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Inductive_reasoning" title="Inductive reasoning">Inductive reasoning</a></div> <p>Inductive reasoning is the process of inferring some <i>general</i> principle <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> from a body of knowledge <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> does not necessarily follow from <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span>. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> might give us very good reason to accept <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> but does not ensure <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span>. For example, if it is given that 95% percent of the elephants are gray, and Louise is an elephant, one can <i>induce</i> that Louise is gray. Still, this is not necessarily the case: 5 percent of the time this conclusion will be wrong.<sup id="cite_ref-:0_7-0" class="reference"><a href="#cite_note-:0-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>However, an inference being derived from statistical data is not sufficient to classify it as inductive. For example, if all swans that a person has observed so far are white, they may instead <i>abduce</i> the possibility that all swans are white. They have good reason to believe the conclusion from the premise because it is the <i>best explanation</i> for their observations, and the truth of the conclusion is still not guaranteed. (Indeed, it turns out that <a href="/wiki/Black_swan" title="Black swan">some swans are black</a>.)<sup id="cite_ref-:0_7-1" class="reference"><a href="#cite_note-:0-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Abduction">Abduction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=4" title="Edit section: Abduction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Abductive reasoning allows inferring <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> as an explanation of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span>. As a result of this inference, abduction allows the precondition <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> to be abducted from the consequence <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span>. <a href="/wiki/Deductive_reasoning" title="Deductive reasoning">Deductive reasoning</a> and abductive reasoning thus differ in which end, left or right, of the proposition "<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span> <a href="/wiki/Entailment" class="mw-redirect" title="Entailment">entails</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span>" serves as conclusion. For example, in a billiard game, after glancing and seeing the eight ball moving towards us, we may abduce that the cue ball struck the eight ball. The strike of the cue ball would account for the movement of the eight ball. It serves as a hypothesis that <i>best explains</i> our observation. Given the many possible explanations for the movement of the eight ball, our abduction does not leave us certain that the cue ball in fact struck the eight ball, but our abduction, still useful, can serve to orient us in our surroundings. Despite many possible explanations for any physical process that we observe, we tend to abduce a single explanation (or a few explanations) for this process in the expectation that we can better orient ourselves in our surroundings and disregard some possibilities. Properly used, abductive reasoning can be a useful source of <a href="/wiki/Prior_probability" title="Prior probability">priors</a> in <a href="/wiki/Bayesian_statistics" title="Bayesian statistics">Bayesian statistics</a>. </p><p>One can understand abductive reasoning as inference to the best explanation,<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> although not all usages of the terms <i>abduction</i> and <i>inference to the best explanation</i> are equivalent.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Formalizations_of_abduction">Formalizations of abduction</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=5" title="Edit section: Formalizations of abduction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Logic-based_abduction">Logic-based abduction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=6" title="Edit section: Logic-based abduction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Logic" title="Logic">logic</a>, <a href="/wiki/Explanation" title="Explanation">explanation</a> is accomplished through the use of a <a href="/wiki/Logical_theory" class="mw-redirect" title="Logical theory">logical theory</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> representing a <a href="/wiki/Domain_of_discourse" title="Domain of discourse">domain</a> and a set of observations <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span>. Abduction is the process of deriving a set of explanations of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span> according to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> and picking out one of those explanations. For <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> to be an explanation of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span> according to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span>, it should satisfy two conditions: </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span> follows from <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span>;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> is consistent with <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span>.</li></ul> <p>In formal logic, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> are assumed to be sets of <a href="/wiki/Literal_(mathematical_logic)" title="Literal (mathematical logic)">literals</a>. The two conditions for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> being an explanation of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span> according to theory <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> are formalized as: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T\cup E\models O;}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>∪</mo> <mi>E</mi> <mo>⊨</mo> <mi>O</mi> <mo>;</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T\cup E\models O;}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4a3cd24071805a735935218c98dd42669e5fc27f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.72ex; height:2.843ex;" alt="{\displaystyle T\cup E\models O;}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T\cup E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> <mo>∪</mo> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T\cup E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5be459373e2cbe878e9ce7c7fcb290cc85ef7da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.994ex; height:2.176ex;" alt="{\displaystyle T\cup E}"></span> is consistent.</dd></dl> <p>Among the possible explanations <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> satisfying these two conditions, some other condition of minimality is usually imposed to avoid irrelevant facts (not contributing to the entailment of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle O}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>O</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle O}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9d70e1d0d87e2ef1092ea1ffe2923d9933ff18fc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.773ex; height:2.176ex;" alt="{\displaystyle O}"></span>) being included in the explanations. Abduction is then the process that picks out some member of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span>. Criteria for picking out a member representing "the best" explanation include the <a href="/wiki/Simplicity" title="Simplicity">simplicity</a>, the <a href="/wiki/Prior_probability" title="Prior probability">prior probability</a>, or the explanatory power of the explanation. </p><p>A <a href="/wiki/Proof_theory" title="Proof theory">proof-theoretical</a> abduction method for <a href="/wiki/First-order_logic" title="First-order logic">first-order</a> classical logic based on the <a href="/wiki/Sequent_calculus" title="Sequent calculus">sequent calculus</a> and a dual one, based on semantic tableaux (<a href="/wiki/Analytic_tableaux" class="mw-redirect" title="Analytic tableaux">analytic tableaux</a>) have been proposed.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> The methods are sound and complete and work for full first-order logic, without requiring any preliminary reduction of formulae into normal forms. These methods have also been extended to <a href="/wiki/Modal_logic" title="Modal logic">modal logic</a>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Abductive_logic_programming" title="Abductive logic programming">Abductive logic programming</a> is a computational framework that extends normal <a href="/wiki/Logic_programming" title="Logic programming">logic programming</a> with abduction. It separates the theory <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> into two components, one of which is a normal logic program, used to generate <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> by means of <a href="/wiki/Backward_reasoning" class="mw-redirect" title="Backward reasoning">backward reasoning</a>, the other of which is a set of integrity constraints, used to filter the set of candidate explanations. </p> <div class="mw-heading mw-heading3"><h3 id="Set-cover_abduction">Set-cover abduction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=7" title="Edit section: Set-cover abduction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A different formalization of abduction is based on inverting the function that calculates the visible effects of the hypotheses. Formally, we are given a set of hypotheses <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/75a9edddcca2f782014371f75dca39d7e13a9c1b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.064ex; height:2.176ex;" alt="{\displaystyle H}"></span> and a set of manifestations <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span>; they are related by the domain knowledge, represented by a function <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cd253103f0876afc68ebead27a5aa9867d927467" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle e}"></span> that takes as an argument a set of hypotheses and gives as a result the corresponding set of manifestations. In other words, for every subset of the hypotheses <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H'\subseteq H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>H</mi> <mo>′</mo> </msup> <mo>⊆</mo> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H'\subseteq H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bc51f9e5939134312fe7f51254750dd173a7102" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.95ex; height:2.676ex;" alt="{\displaystyle H'\subseteq H}"></span>, their effects are known to be <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e(H')}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo stretchy="false">(</mo> <msup> <mi>H</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e(H')}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f0ae9c353fabf3b50d155be177b7e80add48770" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.681ex; height:3.009ex;" alt="{\displaystyle e(H')}"></span>. </p><p>Abduction is performed by finding a set <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H'\subseteq H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>H</mi> <mo>′</mo> </msup> <mo>⊆</mo> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H'\subseteq H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bc51f9e5939134312fe7f51254750dd173a7102" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.95ex; height:2.676ex;" alt="{\displaystyle H'\subseteq H}"></span> such that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M\subseteq e(H')}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> <mo>⊆</mo> <mi>e</mi> <mo stretchy="false">(</mo> <msup> <mi>H</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M\subseteq e(H')}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45d94ed9cef5d4136e4e52635af6e78a658b7a22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.222ex; height:3.009ex;" alt="{\displaystyle M\subseteq e(H')}"></span>. In other words, abduction is performed by finding a set of hypotheses <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>H</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/575e08b1574dc1c2bb8c5941a2a68d6daca7fd8e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.788ex; height:2.509ex;" alt="{\displaystyle H'}"></span> such that their effects <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e(H')}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo stretchy="false">(</mo> <msup> <mi>H</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e(H')}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f0ae9c353fabf3b50d155be177b7e80add48770" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.681ex; height:3.009ex;" alt="{\displaystyle e(H')}"></span> include all observations <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle M}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>M</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle M}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f82cade9898ced02fdd08712e5f0c0151758a0dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.442ex; height:2.176ex;" alt="{\displaystyle M}"></span>. </p><p>A common assumption is that the effects of the hypotheses are independent, that is, for every <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle H'\subseteq H}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>H</mi> <mo>′</mo> </msup> <mo>⊆</mo> <mi>H</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H'\subseteq H}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bc51f9e5939134312fe7f51254750dd173a7102" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.95ex; height:2.676ex;" alt="{\displaystyle H'\subseteq H}"></span>, it holds that <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e(H')=\bigcup _{h\in H'}e(\{h\})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>e</mi> <mo stretchy="false">(</mo> <msup> <mi>H</mi> <mo>′</mo> </msup> <mo stretchy="false">)</mo> <mo>=</mo> <munder> <mo>⋃</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> <mo>∈</mo> <msup> <mi>H</mi> <mo>′</mo> </msup> </mrow> </munder> <mi>e</mi> <mo stretchy="false">(</mo> <mo fence="false" stretchy="false">{</mo> <mi>h</mi> <mo fence="false" stretchy="false">}</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle e(H')=\bigcup _{h\in H'}e(\{h\})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6c48c6eb7d0e3939c4316fcaeab0a8aa8f59889" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.338ex; width:19.785ex; height:5.843ex;" alt="{\displaystyle e(H')=\bigcup _{h\in H'}e(\{h\})}"></span>. If this condition is met, abduction can be seen as a form of <a href="/wiki/Set_covering" class="mw-redirect" title="Set covering">set covering</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Abductive_validation">Abductive validation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=8" title="Edit section: Abductive validation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Abductive validation is the process of validating a given hypothesis through abductive reasoning. This can also be called reasoning through successive approximation.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (July 2020)">citation needed</span></a></i>]</sup> Under this principle, an explanation is valid if it is the best possible explanation of a set of known data. The best possible explanation is often defined in terms of simplicity and elegance (see <a href="/wiki/Occam%27s_razor" title="Occam's razor">Occam's razor</a>). Abductive validation is common practice in hypothesis formation in <a href="/wiki/Science" title="Science">science</a>; moreover, Peirce claims that it is a ubiquitous aspect of thought: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"> <p>Looking out my window this lovely spring morning, I see an azalea in full bloom. No, no! I don't see that; though that is the only way I can describe what I see. That is a proposition, a sentence, a fact; but what I perceive is not proposition, sentence, fact, but only an image, which I make intelligible in part by means of a statement of fact. This statement is abstract; but what I see is concrete. I perform an abduction when I so much as express in a sentence anything I see. The truth is that the whole fabric of our knowledge is one matted felt of pure hypothesis confirmed and refined by induction. Not the smallest advance can be made in knowledge beyond the stage of vacant staring, without making an abduction at every step.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> </blockquote> <p>It was Peirce's own maxim that "Facts cannot be explained by a hypothesis more extraordinary than these facts themselves; and of various hypotheses the least extraordinary must be adopted."<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> After obtaining possible hypotheses that may explain the facts, abductive validation is a method for identifying the most likely hypothesis that should be adopted. </p> <div class="mw-heading mw-heading3"><h3 id="Subjective_logic_abduction">Subjective logic abduction</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=9" title="Edit section: Subjective logic abduction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Subjective_logic" title="Subjective logic">Subjective logic</a> generalises <a href="/wiki/Probabilistic_logic" title="Probabilistic logic">probabilistic logic</a> by including degrees of epistemic <a href="/wiki/Uncertainty_quantification" title="Uncertainty quantification">uncertainty</a> in the input arguments, i.e. instead of probabilities, the analyst can express arguments as <a href="/wiki/Subjective_logic" title="Subjective logic">subjective opinions</a>. Abduction in subjective logic is thus a generalization of probabilistic abduction described above.<sup id="cite_ref-Josang2016-SL_15-0" class="reference"><a href="#cite_note-Josang2016-SL-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> The input arguments in subjective logic are subjective opinions which can be binomial when the opinion applies to a binary variable or multinomial when it applies to an <i>n</i>-ary variable. A subjective opinion thus applies to a state variable <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> which takes its values from a domain <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {X} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">X</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {X} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f75966a2f9d5672136fa9401ee1e75008f95ffd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.019ex; height:2.176ex;" alt="{\displaystyle \mathbf {X} }"></span> (i.e. a state space of exhaustive and mutually disjoint state values <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span>), and is denoted by the tuple <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{X}=(b_{X},u_{X},a_{X})\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{X}=(b_{X},u_{X},a_{X})\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ab1dfa40151e3103ff7e65bd1d7a88aa8208b10" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:18.895ex; height:2.843ex;" alt="{\displaystyle \omega _{X}=(b_{X},u_{X},a_{X})\,\!}"></span>, where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b_{X}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b_{X}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c9fc3c044514ef99296a0402638c816fe06b63b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:3.017ex; height:2.509ex;" alt="{\displaystyle b_{X}\,\!}"></span> is the belief mass distribution over <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {X} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">X</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {X} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f75966a2f9d5672136fa9401ee1e75008f95ffd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.019ex; height:2.176ex;" alt="{\displaystyle \mathbf {X} }"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{X}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{X}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4ba97e0eb25b69f3416678c77d1e752f213be63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:3.349ex; height:2.009ex;" alt="{\displaystyle u_{X}\,\!}"></span> is the epistemic uncertainty mass, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{X}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{X}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7e034f6b23484b575b7fe1f75a0074a752373bb6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:3.249ex; height:2.009ex;" alt="{\displaystyle a_{X}\,\!}"></span> is the <a href="/wiki/Base_rate" title="Base rate">base rate</a> distribution over <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {X} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">X</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {X} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f75966a2f9d5672136fa9401ee1e75008f95ffd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.019ex; height:2.176ex;" alt="{\displaystyle \mathbf {X} }"></span>. These parameters satisfy <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{X}+\sum b_{X}(x)=1\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo>+</mo> <mo>∑</mo> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{X}+\sum b_{X}(x)=1\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86b98d92acdcffc15b2bb66fcab0293c70852046" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; margin-right: -0.387ex; width:19.961ex; height:3.843ex;" alt="{\displaystyle u_{X}+\sum b_{X}(x)=1\,\!}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum a_{X}(x)=1\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∑</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum a_{X}(x)=1\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/acd875d6a211ea7e3ae4d750b9710dba1453cf1d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; margin-right: -0.387ex; width:14.391ex; height:3.843ex;" alt="{\displaystyle \sum a_{X}(x)=1\,\!}"></span> as well as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b_{X}(x),u_{X},a_{X}(x)\in [0,1]\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>,</mo> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>∈</mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b_{X}(x),u_{X},a_{X}(x)\in [0,1]\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b9e34897588c50f9c6c70ba8a3fce7a246e5a4a3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-right: -0.387ex; width:24.68ex; height:2.843ex;" alt="{\displaystyle b_{X}(x),u_{X},a_{X}(x)\in [0,1]\,\!}"></span>. </p><p>Assume the domains <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {X} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">X</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {X} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f75966a2f9d5672136fa9401ee1e75008f95ffd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.019ex; height:2.176ex;" alt="{\displaystyle \mathbf {X} }"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {Y} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">Y</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {Y} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c92a7716a99fadda050469747fce1e475e0ec549" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.019ex; height:2.176ex;" alt="{\displaystyle \mathbf {Y} }"></span> with respective variables <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle X}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>X</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle X}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68baa052181f707c662844a465bfeeb135e82bab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.98ex; height:2.176ex;" alt="{\displaystyle X}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/961d67d6b454b4df2301ac571808a3538b3a6d3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.171ex; width:1.773ex; height:2.009ex;" alt="{\displaystyle Y}"></span>, the set of conditional opinions <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{X\mid Y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>∣</mo> <mi>Y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{X\mid Y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7489a322a9306060d8aa4ebfc89424edbd4ec169" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:4.789ex; height:2.509ex;" alt="{\displaystyle \omega _{X\mid Y}}"></span> (i.e. one conditional opinion for each value <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span>), and the base rate distribution <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a_{Y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{Y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7c8013dd97043499b0e9b182ad37f93a15bfe487" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.716ex; height:2.009ex;" alt="{\displaystyle a_{Y}}"></span>. Based on these parameters, the subjective <a href="/wiki/Bayes%27_theorem" title="Bayes' theorem">Bayes' theorem</a> denoted with the operator <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \;{\widetilde {\phi }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ϕ</mi> <mo>~</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \;{\widetilde {\phi }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1e48b1061a3504657838c0dcddb29eaff3ffe13" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.178ex; height:3.009ex;" alt="{\displaystyle \;{\widetilde {\phi }}}"></span> produces the set of inverted conditionals <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{Y{\tilde {\mid }}X}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo>∣</mo> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mi>X</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{Y{\tilde {\mid }}X}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2dc1d0f18584a44cb8cf1bf599575eb25dbff138" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:5.154ex; height:2.843ex;" alt="{\displaystyle \omega _{Y{\tilde {\mid }}X}}"></span> (i.e. one inverted conditional for each value <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span>) expressed by: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{Y{\tilde {|}}X}=\omega _{X|Y}\;{\widetilde {\phi \,}}\;a_{Y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo stretchy="false">~</mo> </mover> </mrow> </mrow> <mi>X</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>Y</mi> </mrow> </msub> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>ϕ</mi> <mspace width="thinmathspace" /> </mrow> <mo>~</mo> </mover> </mrow> </mrow> <mspace width="thickmathspace" /> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{Y{\tilde {|}}X}=\omega _{X|Y}\;{\widetilde {\phi \,}}\;a_{Y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f47e9200288134c2865f86ad983e77b4385f2790" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.505ex; width:18.821ex; height:3.843ex;" alt="{\displaystyle \omega _{Y{\tilde {|}}X}=\omega _{X|Y}\;{\widetilde {\phi \,}}\;a_{Y}}"></span>.</dd></dl> <p>Using these inverted conditionals together with the opinion <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{X}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{X}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a42947d0b86d4d98a3172ca71d3f1595d296b5a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.078ex; height:2.009ex;" alt="{\displaystyle \omega _{X}}"></span> subjective <a href="/wiki/Deductive_reasoning" title="Deductive reasoning">deduction</a> denoted by the operator <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \circledcirc }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊚</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \circledcirc }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf70a53592b87a725eabcbb2dffc880e9aa9b66c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \circledcirc }"></span> can be used to abduce the marginal opinion <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{Y\,{\overline {\|}}\,X}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo fence="false" stretchy="false">‖</mo> <mo accent="false">¯</mo> </mover> </mrow> <mspace width="thinmathspace" /> <mi>X</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{Y\,{\overline {\|}}\,X}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e2ad178ff592e45944dbeab793caec7488911dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.671ex; width:6.022ex; height:3.009ex;" alt="{\displaystyle \omega _{Y\,{\overline {\|}}\,X}}"></span>. The equality between the different expressions for subjective abduction is given below: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\omega _{Y\,{\widetilde {\|}}\,X}&=\omega _{X\mid Y}\;{\widetilde {\circledcirc }}\;\omega _{X}\\&=(\omega _{X\mid Y}\;{\widetilde {\phi \,}}\;a_{Y})\;\circledcirc \;\omega _{X}\\&=\omega _{Y{\widetilde {|}}X}\;\circledcirc \;\omega _{X}\;.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo fence="false" stretchy="false">‖</mo> <mo>~</mo> </mover> </mrow> </mrow> <mspace width="thinmathspace" /> <mi>X</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>∣</mo> <mi>Y</mi> </mrow> </msub> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo>⊚</mo> <mo>~</mo> </mover> </mrow> </mrow> <mspace width="thickmathspace" /> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> <mo>∣</mo> <mi>Y</mi> </mrow> </msub> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>ϕ</mi> <mspace width="thinmathspace" /> </mrow> <mo>~</mo> </mover> </mrow> </mrow> <mspace width="thickmathspace" /> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mo>⊚</mo> <mspace width="thickmathspace" /> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>Y</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>~</mo> </mover> </mrow> </mrow> <mi>X</mi> </mrow> </msub> <mspace width="thickmathspace" /> <mo>⊚</mo> <mspace width="thickmathspace" /> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>X</mi> </mrow> </msub> <mspace width="thickmathspace" /> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\omega _{Y\,{\widetilde {\|}}\,X}&=\omega _{X\mid Y}\;{\widetilde {\circledcirc }}\;\omega _{X}\\&=(\omega _{X\mid Y}\;{\widetilde {\phi \,}}\;a_{Y})\;\circledcirc \;\omega _{X}\\&=\omega _{Y{\widetilde {|}}X}\;\circledcirc \;\omega _{X}\;.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/097bf3d4d5eff2f00e3cf094da6a692438143d31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.005ex; width:29.365ex; height:11.176ex;" alt="{\displaystyle {\begin{aligned}\omega _{Y\,{\widetilde {\|}}\,X}&=\omega _{X\mid Y}\;{\widetilde {\circledcirc }}\;\omega _{X}\\&=(\omega _{X\mid Y}\;{\widetilde {\phi \,}}\;a_{Y})\;\circledcirc \;\omega _{X}\\&=\omega _{Y{\widetilde {|}}X}\;\circledcirc \;\omega _{X}\;.\end{aligned}}}"></span></dd></dl> <p>The symbolic notation for subjective abduction is "<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\widetilde {\|}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo fence="false" stretchy="false">‖</mo> <mo>~</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\widetilde {\|}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b73af525bb27a02a04db37f20321a047bff81771" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.162ex; height:3.343ex;" alt="{\displaystyle {\widetilde {\|}}}"></span>", and the operator itself is denoted as "<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\widetilde {\circledcirc }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo>⊚</mo> <mo>~</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\widetilde {\circledcirc }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7a8e700c9e81e18bcb7234d6d0af8f4f2152342" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.676ex;" alt="{\displaystyle {\widetilde {\circledcirc }}}"></span>". The operator for the subjective Bayes' theorem is denoted "<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\widetilde {\phi \,}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>ϕ</mi> <mspace width="thinmathspace" /> </mrow> <mo>~</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\widetilde {\phi \,}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9af2f828f79376f9d6fa65884405f4155d4f1acb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.773ex; height:3.009ex;" alt="{\displaystyle {\widetilde {\phi \,}}}"></span>", and subjective deduction is denoted "<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \circledcirc }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊚</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \circledcirc }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf70a53592b87a725eabcbb2dffc880e9aa9b66c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \circledcirc }"></span>".<sup id="cite_ref-Josang2016-SL_15-1" class="reference"><a href="#cite_note-Josang2016-SL-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> </p><p>The advantage of using subjective logic abduction compared to probabilistic abduction is that both aleatoric and epistemic uncertainty about the input argument probabilities can be explicitly expressed and taken into account during the analysis. It is thus possible to perform abductive analysis in the presence of uncertain arguments, which naturally results in degrees of uncertainty in the output conclusions. </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=10" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The idea that the simplest, most easily verifiable solution should be preferred over its more complicated counterparts is a very old one. To this point, <a href="/wiki/George_P%C3%B3lya" title="George Pólya">George Pólya</a>, in his treatise on problem-solving, makes reference to the following Latin truism: <i>simplex sigillum veri</i> (simplicity is the seal of truth).<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Expand_section plainlinks metadata ambox mbox-small-left ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/File:Wiki_letter_w_cropped.svg" class="mw-file-description"><img alt="[icon]" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png" decoding="async" width="20" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/30px-Wiki_letter_w_cropped.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/40px-Wiki_letter_w_cropped.svg.png 2x" data-file-width="44" data-file-height="31" /></a></span></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs expansion</b> with: This deals <i>only</i> with Peirce and no other contributors or critics: other relevant histories should be added, and material that overlaps with the article on Peirce should be removed. You can help by <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Abductive_reasoning&action=edit&section=">adding to it</a>. <span class="date-container"><i>(<span class="date">June 2020</span>)</i></span></div></td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Introduction_and_development_by_Peirce">Introduction and development by Peirce</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=11" title="Edit section: Introduction and development by Peirce"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Overview">Overview</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=12" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The American philosopher Charles Sanders Peirce introduced abduction into modern logic. Over the years he called such inference <i>hypothesis</i>, <i>abduction</i>, <i>presumption</i>, and <i>retroduction</i>. He considered it a topic in logic as a normative field in philosophy, not in purely formal or mathematical logic, and eventually as a topic also in economics of research. </p><p>As two stages of the development, extension, etc., of a hypothesis in scientific <a href="/wiki/Inquiry" title="Inquiry">inquiry</a>, abduction and also <a href="/wiki/Inductive_reasoning" title="Inductive reasoning">induction</a> are often collapsed into one overarching concept—the hypothesis. That is why, in the <a href="/wiki/Scientific_method" title="Scientific method">scientific method</a> known from <a href="/wiki/Galileo_Galilei" title="Galileo Galilei">Galileo</a> and <a href="/wiki/Francis_Bacon" title="Francis Bacon">Bacon</a>, the abductive stage of hypothesis formation is conceptualized simply as induction. Thus, in the twentieth century this collapse was reinforced by <a href="/wiki/Karl_Popper" title="Karl Popper">Karl Popper</a>'s explication of the <a href="/wiki/Hypothetico-deductive_model" title="Hypothetico-deductive model">hypothetico-deductive model</a>, where the hypothesis is considered to be just "a guess"<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> (in the spirit of Peirce). However, when the formation of a hypothesis is considered the result of a process it becomes clear that this "guess" has already been tried and made more robust in thought as a necessary stage of its acquiring the status of hypothesis. Indeed, many abductions are rejected or heavily modified by subsequent abductions before they ever reach this stage. </p><p>Before 1900, Peirce treated abduction as the use of a known rule to explain an observation. For instance: it is a known rule that, if it rains, grass gets wet; so, to explain the fact that the grass on this lawn is wet, one <i>abduces</i> that it has rained. Abduction can lead to false conclusions if other rules that might explain the observation are not taken into account—e.g. the grass could be wet from <a href="/wiki/Dew" title="Dew">dew</a>. This remains the common use of the term "abduction" in the <a href="/wiki/Social_science" title="Social science">social sciences</a> and in <a href="/wiki/Artificial_intelligence" title="Artificial intelligence">artificial intelligence</a>. </p><p>Peirce consistently characterized it as the kind of inference that originates a hypothesis by concluding in an explanation, though an unassured one, for some very curious or surprising (anomalous) observation stated in a premise. As early as 1865 he wrote that all conceptions of cause and force are reached through hypothetical inference; in the 1900s he wrote that all explanatory content of theories is reached through abduction. In other respects Peirce revised his view of abduction over the years.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p><p>In later years his view came to be: </p> <ul><li>Abduction is guessing.<sup id="cite_ref-guess_19-0" class="reference"><a href="#cite_note-guess-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> It is "very little hampered" by rules of logic.<sup id="cite_ref-HL_20-0" class="reference"><a href="#cite_note-HL-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> Even a well-prepared mind's individual guesses are more frequently wrong than right.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> But the success of our guesses far exceeds that of random luck and seems born of attunement to nature by instinct<sup id="cite_ref-NA_22-0" class="reference"><a href="#cite_note-NA-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> (some speak of <a href="/wiki/Logical_intuition" title="Logical intuition">intuition</a> in such contexts<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup>).</li> <li>Abduction guesses a new or outside idea so as to account in a plausible, instinctive, economical way for a surprising or very complicated phenomenon. That is its proximate aim.<sup id="cite_ref-NA_22-1" class="reference"><a href="#cite_note-NA-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></li> <li>Its longer aim is to economize <a href="/wiki/Inquiry" title="Inquiry">inquiry</a> itself. Its rationale is inductive: it works often enough, is the only source of new ideas, and has no substitute in expediting the discovery of new truths.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> Its rationale especially involves its role in coordination with other modes of inference in inquiry. It is inference to explanatory hypotheses for selection of those best worth trying.</li> <li><a href="/wiki/Pragmatism" title="Pragmatism">Pragmatism</a> is the logic of abduction. Upon the generation of an explanation (which he came to regard as instinctively guided), the <a href="/wiki/Pragmatic_maxim" title="Pragmatic maxim">pragmatic maxim</a> gives the necessary and sufficient logical rule to abduction in general. The hypothesis, being insecure, needs to have conceivable<sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> implications for informed practice, so as to be testable<sup id="cite_ref-L75_26-0" class="reference"><a href="#cite_note-L75-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-prag_27-0" class="reference"><a href="#cite_note-prag-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> and, through its trials, to expedite and economize inquiry. The economy of research is what calls for abduction and governs its art.<sup id="cite_ref-econ_28-0" class="reference"><a href="#cite_note-econ-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup></li></ul> <p>Writing in 1910, Peirce admits that "in almost everything I printed before the beginning of this century I more or less mixed up hypothesis and induction" and he traces the confusion of these two types of reasoning to logicians' too "narrow and formalistic a conception of inference, as necessarily having formulated judgments from its premises."<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p><p>He started out in the 1860s treating hypothetical inference in a number of ways which he eventually peeled away as inessential or, in some cases, mistaken: </p> <ul><li>as inferring the occurrence of a character (a characteristic) from the observed combined occurrence of multiple characters which its occurrence would necessarily involve;<sup id="cite_ref-NCA_30-0" class="reference"><a href="#cite_note-NCA-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> for example, if any occurrence of <i>A</i> is known to necessitate occurrence of <i>B, C, D, E</i>, then the observation of <i>B, C, D, E</i> suggests by way of explanation the occurrence of <i>A</i>. (But by 1878 he no longer regarded such multiplicity as common to all hypothetical inference.<sup id="cite_ref-DIH_31-0" class="reference"><a href="#cite_note-DIH-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><a class="external text" href="https://en.wikisource.org/wiki/Popular_Science_Monthly/Volume_13/August_1878/Illustrations_of_the_Logic_of_Science_VI">Wikisource</a>)</li> <li>as aiming for a more or less probable hypothesis (in 1867 and 1883 but not in 1878; anyway by 1900 the justification is not probability but the lack of alternatives to guessing and the fact that guessing is fruitful;<sup id="cite_ref-L2L_32-0" class="reference"><a href="#cite_note-L2L-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> by 1903 he speaks of the "likely" in the sense of nearing the truth in an "indefinite sense";<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> by 1908 he discusses <i>plausibility</i> as instinctive appeal.<sup id="cite_ref-NA_22-2" class="reference"><a href="#cite_note-NA-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup>) In a paper dated by editors as <i>circa</i> 1901, he discusses "instinct" and "naturalness", along with the kind of considerations (low cost of testing, logical caution, breadth, and incomplexity) that he later calls methodeutical.<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup></li> <li>as induction from characters (but as early as 1900 he characterized abduction as guessing<sup id="cite_ref-L2L_32-1" class="reference"><a href="#cite_note-L2L-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup>)</li> <li>as citing a known rule in a premise rather than hypothesizing a rule in the conclusion (but by 1903 he allowed either approach<sup id="cite_ref-HL_20-1" class="reference"><a href="#cite_note-HL-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-newidea_35-0" class="reference"><a href="#cite_note-newidea-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup>)</li> <li>as basically a transformation of a deductive categorical syllogism<sup id="cite_ref-DIH_31-1" class="reference"><a href="#cite_note-DIH-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> (but in 1903 he offered a variation on <i>modus ponens</i> instead,<sup id="cite_ref-HL_20-2" class="reference"><a href="#cite_note-HL-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> and by 1911 he was unconvinced that any one form covers all hypothetical inference<sup id="cite_ref-kehler_36-0" class="reference"><a href="#cite_note-kehler-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup>).</li></ul> <div class="mw-heading mw-heading4"><h4 id="The_Natural_Classification_of_Arguments_(1867)"><span id="The_Natural_Classification_of_Arguments_.281867.29"></span><i>The Natural Classification of Arguments</i> (1867)</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=13" title="Edit section: The Natural Classification of Arguments (1867)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1867, Peirce's "On the Natural Classification of Arguments",<sup id="cite_ref-NCA_30-1" class="reference"><a href="#cite_note-NCA-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> hypothetical inference always deals with a cluster of characters (call them <i>P′, P′′, P′′′,</i> etc.) known to occur at least whenever a certain character (<i>M</i>) occurs. Note that categorical syllogisms have elements traditionally called middles, predicates, and subjects. For example: All <i>men</i> [middle] are <i>mortal</i> [predicate]; <i>Socrates</i> [subject] is a <i>man</i> [middle]; ergo <i>Socrates</i> [subject] is <i>mortal</i> [predicate]". Below, 'M' stands for a middle; 'P' for a predicate; 'S' for a subject. Peirce held that all deduction can be put into the form of the categorical <a href="/wiki/Syllogism" title="Syllogism">syllogism</a> <a href="/wiki/Syllogism#Barbara_(AAA-1)" title="Syllogism">Barbara (AAA-1)</a>. </p> <blockquote> <table cellspacing="1" cellpadding="7" style="background-color:#999"> <tbody><tr style="vertical-align:top;background-color:#fff"> <td>[Deduction]. <p>[Any] M is P <br /> [Any] S is M <br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \therefore }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∴</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \therefore }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbb8b7f072bd54b28a08d8f7ad207f9df1bf9f22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.55ex; height:1.843ex;" alt="{\displaystyle \therefore }"></span> [Any] S is P. </p> </td> <td>Induction. <p><i>S′, S′′, S′′′</i>, &c. are taken at random as <i>M'</i>s; <br /> <i>S′, S′′, S′′′</i>, &c. are <i>P</i>: <br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \therefore }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∴</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \therefore }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbb8b7f072bd54b28a08d8f7ad207f9df1bf9f22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.55ex; height:1.843ex;" alt="{\displaystyle \therefore }"></span> Any <i>M</i> is probably <i>P</i>. </p> </td> <td>Hypothesis. <p>Any <i>M</i> is, for instance, <i>P′, P′′, P′′′,</i> &c.; <br /> <i>S</i> is <i>P′, P′′, P′′′,</i> &c.: <br /> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \therefore }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∴</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \therefore }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbb8b7f072bd54b28a08d8f7ad207f9df1bf9f22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.55ex; height:1.843ex;" alt="{\displaystyle \therefore }"></span> <i>S</i> is probably <i>M</i>. </p> </td></tr></tbody></table> </blockquote> <div class="mw-heading mw-heading4"><h4 id="Deduction,_Induction,_and_Hypothesis_(1878)"><span id="Deduction.2C_Induction.2C_and_Hypothesis_.281878.29"></span><i>Deduction, Induction, and Hypothesis</i> (1878)</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=14" title="Edit section: Deduction, Induction, and Hypothesis (1878)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1878, in "Deduction, Induction, and Hypothesis",<sup id="cite_ref-DIH_31-2" class="reference"><a href="#cite_note-DIH-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> there is no longer a need for multiple characters or predicates in order for an inference to be hypothetical, although it is still helpful. Moreover, Peirce no longer poses hypothetical inference as concluding in a <i>probable</i> hypothesis. In the forms themselves, it is understood but not explicit that induction involves random selection and that hypothetical inference involves response to a "very curious circumstance". The forms instead emphasize the modes of inference as rearrangements of one another's propositions (without the bracketed hints shown below). </p> <table cellspacing="1" cellpadding="3" style="background-color:#999"> <tbody><tr valign="top" style="background-color:#fff"> <td>Deduction. <p><i>Rule:</i> All the beans from this bag are white. <br /><i>Case:</i> These beans are from this bag. <br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \therefore }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∴</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \therefore }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbb8b7f072bd54b28a08d8f7ad207f9df1bf9f22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.55ex; height:1.843ex;" alt="{\displaystyle \therefore }"></span> <i>Result:</i> These beans are white. </p> </td> <td>Induction. <p><i>Case:</i> These beans are [randomly selected] from this bag. <br /><i>Result:</i> These beans are white. <br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \therefore }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∴</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \therefore }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbb8b7f072bd54b28a08d8f7ad207f9df1bf9f22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.55ex; height:1.843ex;" alt="{\displaystyle \therefore }"></span> <i>Rule:</i> All the beans from this bag are white. </p> </td> <td>Hypothesis. <p><i>Rule:</i> All the beans from this bag are white. <br /><i>Result:</i> These beans [oddly] are white. <br /><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \therefore }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∴</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \therefore }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbb8b7f072bd54b28a08d8f7ad207f9df1bf9f22" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.55ex; height:1.843ex;" alt="{\displaystyle \therefore }"></span> <i>Case:</i> These beans are from this bag. </p> </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="A_Theory_of_Probable_Inference_(1883)"><span id="A_Theory_of_Probable_Inference_.281883.29"></span><i>A Theory of Probable Inference</i> (1883)</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=15" title="Edit section: A Theory of Probable Inference (1883)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Peirce long treated abduction in terms of induction from characters or traits (weighed, not counted like objects), explicitly so in his influential 1883 "A theory of probable inference", in which he returns to involving probability in the hypothetical conclusion.<sup id="cite_ref-Pierce-1883_37-0" class="reference"><a href="#cite_note-Pierce-1883-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> Like "Deduction, Induction, and Hypothesis" in 1878, it was widely read (see the historical books on statistics by <a href="/wiki/Stephen_Stigler" title="Stephen Stigler">Stephen Stigler</a>), unlike his later amendments of his conception of abduction. Today abduction remains most commonly understood as induction from characters and extension of a known rule to cover unexplained circumstances. </p><p><a href="/wiki/Sherlock_Holmes" title="Sherlock Holmes">Sherlock Holmes</a> used this method of reasoning in the stories of <a href="/wiki/Arthur_Conan_Doyle" title="Arthur Conan Doyle">Arthur Conan Doyle</a>, although Holmes refers to it as "<a href="/wiki/Deductive_reasoning" title="Deductive reasoning">deductive reasoning</a>".<sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Minute_Logic_(1902)_and_after"><span id="Minute_Logic_.281902.29_and_after"></span><i>Minute Logic</i> (1902) and after</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=16" title="Edit section: Minute Logic (1902) and after"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1902 Peirce wrote that he now regarded the syllogistical forms and the doctrine of extension and comprehension (i.e., objects and characters as referenced by terms), as being less fundamental than he had earlier thought.<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> In 1903 he offered the following form for abduction:<sup id="cite_ref-HL_20-3" class="reference"><a href="#cite_note-HL-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>The surprising fact, C, is observed; </p><dl><dd>But if A were true, C would be a matter of course,</dd> <dd>Hence, there is reason to suspect that A is true.</dd></dl></blockquote> <p>The hypothesis is framed, but not asserted, in a premise, then asserted as rationally suspectable in the conclusion. Thus, as in the earlier categorical syllogistic form, the conclusion is formulated from some premise(s). But all the same the hypothesis consists more clearly than ever in a new or outside idea beyond what is known or observed. Induction in a sense goes beyond observations already reported in the premises, but it merely amplifies ideas already known to represent occurrences, or tests an idea supplied by hypothesis; either way it requires previous abductions in order to get such ideas in the first place. Induction seeks facts to test a hypothesis; abduction seeks a hypothesis to account for facts. </p><p>Note that the hypothesis ("A") could be of a rule. It need not even be a rule strictly necessitating the surprising observation ("C"), which needs to follow only as a "matter of course"; or the "course" itself could amount to some known rule, merely alluded to, and also not necessarily a rule of strict necessity. In the same year, Peirce wrote that reaching a hypothesis may involve placing a surprising observation under either a newly hypothesized rule or a hypothesized combination of a known rule with a peculiar state of facts, so that the phenomenon would be not surprising but instead either necessarily implied or at least likely.<sup id="cite_ref-newidea_35-1" class="reference"><a href="#cite_note-newidea-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> </p><p>Peirce did not remain quite convinced about any such form as the categorical syllogistic form or the 1903 form. In 1911, he wrote, "I do not, at present, feel quite convinced that any logical form can be assigned that will cover all 'Retroductions'. For what I mean by a Retroduction is simply a conjecture which arises in the mind."<sup id="cite_ref-kehler_36-1" class="reference"><a href="#cite_note-kehler-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Pragmatism">Pragmatism</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=17" title="Edit section: Pragmatism"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1901 Peirce wrote, "There would be no logic in imposing rules, and saying that they ought to be followed, until it is made out that the purpose of hypothesis requires them."<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> In 1903 Peirce called <a href="/wiki/Pragmatism" title="Pragmatism">pragmatism</a> "the logic of abduction" and said that the <a href="/wiki/Pragmatic_maxim" title="Pragmatic maxim">pragmatic maxim</a> gives the necessary and sufficient logical rule to abduction in general.<sup id="cite_ref-prag_27-1" class="reference"><a href="#cite_note-prag-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> The pragmatic maxim is: </p> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object.</p></blockquote> <p>It is a method for fruitful clarification of conceptions by equating the meaning of a conception with the conceivable practical implications of its object's conceived effects. Peirce held that that is precisely tailored to abduction's purpose in inquiry, the forming of an idea that could conceivably shape informed conduct. In various writings in the 1900s<sup id="cite_ref-econ_28-1" class="reference"><a href="#cite_note-econ-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-43" class="reference"><a href="#cite_note-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> he said that the conduct of abduction (or retroduction) is governed by considerations of economy, belonging in particular to the economics of research. He regarded economics as a normative science whose analytic portion might be part of logical methodeutic (that is, theory of inquiry).<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Three_levels_of_logic_about_abduction">Three levels of logic about abduction</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=18" title="Edit section: Three levels of logic about abduction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Peirce came over the years to <a href="/wiki/Classification_of_the_sciences_(Peirce)#Sciences" title="Classification of the sciences (Peirce)">divide (philosophical) logic</a> into three departments: </p> <ol><li>Stechiology, or speculative grammar, on the conditions for meaningfulness. Classification of signs (semblances, symptoms, symbols, etc.) and their combinations (as well as their objects and <a href="/wiki/Interpretant" title="Interpretant">interpretants</a>).</li> <li>Logical critic, or logic proper, on validity or justifiability of inference, the conditions for true representation. Critique of arguments in their various modes (deduction, induction, abduction).</li> <li>Methodeutic, or speculative rhetoric, on the conditions for determination of interpretations. Methodology of inquiry in its interplay of modes.</li></ol> <p>Peirce had, from the start, seen the modes of inference as being coordinated together in scientific inquiry and, by the 1900s, held that hypothetical inference in particular is inadequately treated at the level of critique of arguments.<sup id="cite_ref-L75_26-1" class="reference"><a href="#cite_note-L75-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-prag_27-2" class="reference"><a href="#cite_note-prag-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> To increase the assurance of a hypothetical conclusion, one needs to deduce implications about evidence to be found, predictions which induction can test through observation so as to evaluate the hypothesis. That is <a href="/wiki/Charles_Sanders_Peirce#Scientific_method" title="Charles Sanders Peirce">Peirce's outline of the scientific method</a> of inquiry, as covered in his inquiry methodology, which includes <a href="/wiki/Pragmatism" title="Pragmatism">pragmatism</a> or, as he later called it, <a href="/wiki/Pragmaticism" title="Pragmaticism">pragmaticism</a>, the clarification of ideas in terms of their conceivable implications regarding informed practice. </p> <div class="mw-heading mw-heading5"><h5 id="Classification_of_signs">Classification of signs</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=19" title="Edit section: Classification of signs"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>As early as 1866,<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> Peirce held that: </p><p>1. Hypothesis (abductive inference) is inference through an <i>icon</i> (also called a <i>likeness</i>). <br /> 2. Induction is inference through an <i>index</i> (a sign by factual connection); a sample is an index of the totality from which it is drawn. <br /> 3. Deduction is inference through a <i>symbol</i> (a sign by interpretive habit irrespective of resemblance or connection to its object). </p><p>In 1902, Peirce wrote that, in abduction: "It is recognized that the phenomena are <i>like</i>, i.e. constitute an Icon of, a replica of a general conception, or Symbol."<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading5"><h5 id="Critique_of_arguments">Critique of arguments</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=20" title="Edit section: Critique of arguments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>At the critical level Peirce examined the forms of abductive arguments (as discussed above), and came to hold that the hypothesis should economize explanation for plausibility in terms of the feasible and natural. In 1908 Peirce described this plausibility in some detail.<sup id="cite_ref-NA_22-3" class="reference"><a href="#cite_note-NA-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> It involves not likeliness based on observations (which is instead the inductive evaluation of a hypothesis), but instead optimal simplicity in the sense of the "facile and natural", as by Galileo's natural light of reason and as distinct from "logical simplicity" (Peirce does not dismiss logical simplicity entirely but sees it in a subordinate role; taken to its logical extreme it would favor adding no explanation to the observation at all). Even a well-prepared mind guesses oftener wrong than right, but our guesses succeed better than random luck at reaching the truth or at least advancing the inquiry, and that indicates to Peirce that they are based in instinctive attunement to nature, an affinity between the mind's processes and the processes of the real, which would account for why appealingly "natural" guesses are the ones that oftenest (or least seldom) succeed; to which Peirce added the argument that such guesses are to be preferred since, without "a natural bent like nature's", people would have no hope of understanding nature. In 1910 Peirce made a three-way distinction between probability, verisimilitude, and plausibility, and defined plausibility with a normative "ought": "By plausibility, I mean the degree to which a theory ought to recommend itself to our belief independently of any kind of evidence other than our instinct urging us to regard it favorably."<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup> For Peirce, plausibility does not depend on observed frequencies or probabilities, or on verisimilitude, or even on testability, which is not a question of the critique of the hypothetical inference <i>as</i> an inference, but rather a question of the hypothesis's relation to the inquiry process. </p><p>The phrase "inference to the best explanation" (not used by Peirce but often applied to hypothetical inference) is not always understood as referring to the most simple and natural hypotheses (such as those with the <a href="/wiki/Occam%27s_razor" title="Occam's razor">fewest assumptions</a>). However, in other senses of "best", such as "standing up best to tests", it is hard to know which is the best explanation to form, since one has not tested it yet. Still, for Peirce, any justification of an abductive inference as "good" is not completed upon its formation as an argument (unlike with induction and deduction) and instead depends also on its methodological role and promise (such as its testability) in advancing inquiry.<sup id="cite_ref-L75_26-2" class="reference"><a href="#cite_note-L75-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-prag_27-3" class="reference"><a href="#cite_note-prag-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading5"><h5 id="Methodology_of_inquiry">Methodology of inquiry</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=21" title="Edit section: Methodology of inquiry"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>At the methodeutical level Peirce held that a hypothesis is judged and selected<sup id="cite_ref-L75_26-3" class="reference"><a href="#cite_note-L75-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> for testing because it offers, via its trial, to expedite and economize the <a href="/wiki/Inquiry" title="Inquiry">inquiry</a> process itself toward new truths, first of all by being testable and also by further economies,<sup id="cite_ref-econ_28-2" class="reference"><a href="#cite_note-econ-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> in terms of cost, value, and relationships among guesses (hypotheses). Here, considerations such as probability, absent from the treatment of abduction at the critical level, come into play. For examples: </p> <ul><li>Cost: A simple but low-odds guess, if low in cost to test for falsity, may belong first in line for testing, to get it out of the way. If surprisingly it stands up to tests, that is worth knowing early in the inquiry, which otherwise might have stayed long on a wrong though seemingly likelier track.</li> <li>Value: A guess is intrinsically worth testing if it has instinctual plausibility or reasoned objective probability, while <a href="/wiki/Subjective_probability" class="mw-redirect" title="Subjective probability">subjective likelihood</a>, though reasoned, can be treacherous.</li> <li>Interrelationships: Guesses can be chosen for trial strategically for their <ul><li><i>caution</i>, for which Peirce gave as an example the game of <a href="/wiki/Twenty_Questions" class="mw-redirect" title="Twenty Questions">Twenty Questions</a>,</li> <li><i>breadth</i> of applicability to explain various phenomena, and</li> <li><i>incomplexity</i>, that of a hypothesis that seems too simple but whose trial "may give a good 'leave', as the billiard-players say", and be instructive for the pursuit of various and conflicting hypotheses that are less simple.<sup id="cite_ref-econ2_49-0" class="reference"><a href="#cite_note-econ2-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup></li></ul></li></ul> <div class="mw-heading mw-heading4"><h4 id="Uberty">Uberty</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=22" title="Edit section: Uberty"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Peirce<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup> indicated that abductive reasoning is driven by the need for "economy in research"—the expected fact-based productivity of hypotheses, prior to deductive and inductive processes of verification. A key concept proposed by him in this regard is "<a href="https://en.wiktionary.org/wiki/uberty" class="extiw" title="wiktionary:uberty">uberty</a>"<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup>—the expected fertility and pragmatic value of reasoning. This concept seems to be gaining support via association to the <a href="/wiki/Free_energy_principle" title="Free energy principle">Free Energy Principle</a>.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Gilbert_Harman_(1965)"><span id="Gilbert_Harman_.281965.29"></span>Gilbert Harman (1965)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=23" title="Edit section: Gilbert Harman (1965)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Gilbert_Harman" title="Gilbert Harman">Gilbert Harman</a> was a professor of philosophy at <a href="/wiki/Princeton_University" title="Princeton University">Princeton University</a>. Harman's 1965 account of the role of "inference to the best explanation" – inferring the existence of that which we need for the best explanation of observable phenomena – has been very influential. </p> <div class="mw-heading mw-heading3"><h3 id="Stephen_Jay_Gould_(1995)"><span id="Stephen_Jay_Gould_.281995.29"></span>Stephen Jay Gould (1995)</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=24" title="Edit section: Stephen Jay Gould (1995)"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Stephen_Jay_Gould" title="Stephen Jay Gould">Stephen Jay Gould</a>, in answering the <a href="/wiki/Omphalos_hypothesis" title="Omphalos hypothesis">Omphalos hypothesis</a>, claimed that only hypotheses that can be proved incorrect lie within the domain of <a href="/wiki/Science" title="Science">science</a> and only these hypotheses are good explanations of facts worth inferring to.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"></p><blockquote class="templatequote"><p>"[W]hat is so desperately wrong with Omphalos? Only this really (and perhaps paradoxically): that we can devise no way to find out whether it is wrong—or for that matter, right. Omphalos is the classic example of an utterly untestable notion, for the world will look exactly the same in all its intricate detail whether fossils and strata are prochronic [signs of a fictitious past] or products of an extended history. . . . Science is a procedure for testing and rejecting hypotheses, not a compendium of certain knowledge. Claims that can be proved incorrect lie within its domain. . . . But theories that cannot be tested in principle are not part of science. . . . [W]e reject Omphalos as useless, not wrong."</p></blockquote> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=25" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Artificial_intelligence">Artificial intelligence</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=26" title="Edit section: Artificial intelligence"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Applications in <a href="/wiki/Artificial_intelligence" title="Artificial intelligence">artificial intelligence</a> include <a href="/wiki/Diagnosis_(artificial_intelligence)" title="Diagnosis (artificial intelligence)">fault diagnosis</a>, <a href="/wiki/Belief_revision" title="Belief revision">belief revision</a>, and <a href="/wiki/Automated_planning" class="mw-redirect" title="Automated planning">automated planning</a>. The most direct application of abduction is that of automatically detecting faults in systems: given a theory relating faults with their effects and a set of observed effects, abduction can be used to derive sets of faults that are likely to be the cause of the problem.<sup id="cite_ref-Josephson,_Magnani_4-1" class="reference"><a href="#cite_note-Josephson,_Magnani-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Medicine">Medicine</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=27" title="Edit section: Medicine"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Medicine" title="Medicine">medicine</a>, abduction can be seen as a component of clinical evaluation and judgment.<sup id="cite_ref-Rapezzi2005_54-0" class="reference"><a href="#cite_note-Rapezzi2005-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Rejon2012_55-0" class="reference"><a href="#cite_note-Rejon2012-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Internist-I" title="Internist-I">Internist-I</a> diagnostic system, the first <a href="/wiki/AI" class="mw-redirect" title="AI">AI</a> system that covered the field of Internal Medicine, used abductive reasoning to converge on the most likely causes of a set of patient symptoms that it acquired through an interactive dialog with an expert user.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Automated_planning">Automated planning</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=28" title="Edit section: Automated planning"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Abduction can also be used to model <a href="/wiki/Automated_planning" class="mw-redirect" title="Automated planning">automated planning</a>.<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup> Given a logical theory relating action occurrences with their effects (for example, a formula of the <a href="/wiki/Event_calculus" title="Event calculus">event calculus</a>), the problem of finding a plan for reaching a state can be modeled as the problem of abducting a set of literals implying that the final state is the goal state. </p> <div class="mw-heading mw-heading3"><h3 id="Intelligence_analysis">Intelligence analysis</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=29" title="Edit section: Intelligence analysis"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Intelligence_analysis" title="Intelligence analysis">intelligence analysis</a>, <a href="/wiki/Analysis_of_competing_hypotheses" title="Analysis of competing hypotheses">analysis of competing hypotheses</a> and <a href="/wiki/Bayesian_network" title="Bayesian network">Bayesian networks</a>, probabilistic abductive reasoning is used extensively. Similarly in <a href="/wiki/Medical_diagnosis" title="Medical diagnosis">medical diagnosis</a> and legal reasoning, the same methods are being used, although there have been many examples of errors, especially caused by the <a href="/wiki/Base_rate_fallacy" title="Base rate fallacy">base rate fallacy</a> and the <a href="/wiki/Prosecutor%27s_fallacy" class="mw-redirect" title="Prosecutor's fallacy">prosecutor's fallacy</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Belief_revision">Belief revision</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=30" title="Edit section: Belief revision"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1251242444"><table class="box-Unreferenced_section plainlinks metadata ambox mbox-small-left ambox-content ambox-Unreferenced" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></td><td class="mbox-text"><div class="mbox-text-span">This section <b>does not <a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources">cite</a> any <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">sources</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Abductive_reasoning" title="Special:EditPage/Abductive reasoning">improve this section</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and <a href="/wiki/Wikipedia:Verifiability#Burden_of_evidence" title="Wikipedia:Verifiability">removed</a>.</span> <span class="date-container"><i>(<span class="date">January 2019</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p><a href="/wiki/Belief_revision" title="Belief revision">Belief revision</a>, the process of adapting beliefs in view of new information, is another field in which abduction has been applied. The main problem of belief revision is that the new information may be inconsistent with the prior <a href="/wiki/Web_of_belief" class="mw-redirect" title="Web of belief">web of beliefs</a>, while the result of the incorporation cannot be inconsistent. The process of updating the web of beliefs can be done by the use of abduction: once an explanation for the observation has been found, integrating it does not generate inconsistency. </p><p>Gärdenfors’ paper<sup id="cite_ref-Gärdenfors_58-0" class="reference"><a href="#cite_note-Gärdenfors-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> contains a brief survey of the area of belief revision and its relation to updating of logical databases, and explores the relationship between belief revision and nonmonotonic logic. </p><p>This use of abduction is not straightforward, as adding <a href="/wiki/Propositional_formula" title="Propositional formula">propositional formulae</a> to other propositional formulae can only make inconsistencies worse. Instead, abduction is done at the level of the ordering of preference of the <a href="/wiki/Possible_world" title="Possible world">possible worlds</a>. Preference models use <a href="/wiki/Fuzzy_logic" title="Fuzzy logic">fuzzy logic</a> or <a href="/wiki/Utility_models" class="mw-redirect" title="Utility models">utility models</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Philosophy_of_science">Philosophy of science</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=31" title="Edit section: Philosophy of science"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In the <a href="/wiki/Philosophy_of_science" title="Philosophy of science">philosophy of science</a>, abduction has been the key inference method to support <a href="/wiki/Scientific_realism" title="Scientific realism">scientific realism</a>, and much of the debate about scientific realism is focused on whether abduction is an acceptable method of inference.<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Historical_linguistics">Historical linguistics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=32" title="Edit section: Historical linguistics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Historical_linguistics" title="Historical linguistics">historical linguistics</a>, abduction during language acquisition is often taken to be an essential part of processes of <a href="/wiki/Language_change" title="Language change">language change</a> such as reanalysis and <a href="/wiki/Analogy" title="Analogy">analogy</a>.<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Applied_linguistics">Applied linguistics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=33" title="Edit section: Applied linguistics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Applied_linguistics" title="Applied linguistics">applied linguistics</a> research, abductive reasoning is starting to be used as an alternative explanation to inductive reasoning, in recognition of anticipated outcomes of qualitative inquiry playing a role in shaping the direction of analysis. It is defined as "The use of an unclear premise based on observations, pursuing theories to try to explain it" (Rose et al., 2020, p. 258)<sup id="cite_ref-61" class="reference"><a href="#cite_note-61"><span class="cite-bracket">[</span>61<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-62" class="reference"><a href="#cite_note-62"><span class="cite-bracket">[</span>62<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Anthropology">Anthropology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=34" title="Edit section: Anthropology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Anthropology" title="Anthropology">anthropology</a>, <a href="/wiki/Alfred_Gell" title="Alfred Gell">Alfred Gell</a> in his influential book <i>Art and Agency</i> defined abduction (after Eco<sup id="cite_ref-63" class="reference"><a href="#cite_note-63"><span class="cite-bracket">[</span>63<span class="cite-bracket">]</span></a></sup>) as "a case of synthetic inference 'where we find some very curious circumstances, which would be explained by the supposition that it was a case of some general rule, and thereupon adopt that supposition<span style="padding-right:.15em;">'</span>".<sup id="cite_ref-Gell,_A_1984,_p_14_64-0" class="reference"><a href="#cite_note-Gell,_A_1984,_p_14-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> Gell criticizes existing "anthropological" studies of art for being too preoccupied with aesthetic value and not preoccupied enough with the central anthropological concern of uncovering "social relationships", specifically the social contexts in which artworks are produced, circulated, and received.<sup id="cite_ref-65" class="reference"><a href="#cite_note-65"><span class="cite-bracket">[</span>65<span class="cite-bracket">]</span></a></sup> Abduction is used as the mechanism for getting from art to agency. That is, abduction can explain how works of art inspire a <i>sensus communis:</i> the commonly held views shared by members that characterize a given society.<sup id="cite_ref-University_of_California,_Berkeley_66-0" class="reference"><a href="#cite_note-University_of_California,_Berkeley-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup> </p><p>The question Gell asks in the book is, "how does it initially 'speak' to people?" He answers by saying that "No reasonable person could suppose that art-like relations between people and things do not involve at least some form of <a href="/wiki/Semiosis" title="Semiosis">semiosis</a>."<sup id="cite_ref-Gell,_A_1984,_p_14_64-1" class="reference"><a href="#cite_note-Gell,_A_1984,_p_14-64"><span class="cite-bracket">[</span>64<span class="cite-bracket">]</span></a></sup> However, he rejects any intimation that semiosis can be thought of as a language because then he would have to admit to some pre-established existence of the <i>sensus communis</i> that he wants to claim only emerges afterwards out of art. Abduction is the answer to this conundrum because the tentative nature of the abduction concept (Peirce likened it to guessing) means that not only can it operate outside of any pre-existing framework, but moreover, it can actually intimate the existence of a framework. As Gell reasons in his analysis, the physical existence of the artwork prompts the viewer to perform an abduction that imbues the artwork with intentionality. A statue of a goddess, for example, in some senses actually becomes the goddess in the mind of the beholder; and represents not only the form of the deity but also her intentions (which are adduced from the feeling of her very presence). Therefore, through abduction, Gell claims that art can have the kind of agency that plants the seeds that grow into cultural myths. The power of agency is the power to motivate actions and inspire ultimately the shared understanding that characterizes any given society.<sup id="cite_ref-University_of_California,_Berkeley_66-1" class="reference"><a href="#cite_note-University_of_California,_Berkeley-66"><span class="cite-bracket">[</span>66<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Computer_programming">Computer programming</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=35" title="Edit section: Computer programming"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/Formal_methods" title="Formal methods">formal methods</a>, logic is used to specify and prove properties of computer programs. Abduction has been used in mechanized reasoning tools to increase the level of automation of the proof activity. </p><p>A technique known as bi-abduction, which mixes abduction and the <a href="/wiki/Frame_problem" title="Frame problem">frame problem</a>, was used to scale reasoning techniques for memory properties to millions of lines of code;<sup id="cite_ref-67" class="reference"><a href="#cite_note-67"><span class="cite-bracket">[</span>67<span class="cite-bracket">]</span></a></sup> logic-based abduction was used to infer pre-conditions for individual functions in a program, relieving the human of the need to do so. It led to a program-proof startup company, which was acquired by Facebook,<sup id="cite_ref-68" class="reference"><a href="#cite_note-68"><span class="cite-bracket">[</span>68<span class="cite-bracket">]</span></a></sup> and the Infer program analysis tool, which led to thousands of bugs being prevented in industrial codebases.<sup id="cite_ref-69" class="reference"><a href="#cite_note-69"><span class="cite-bracket">[</span>69<span class="cite-bracket">]</span></a></sup> </p><p>In addition to inference of function preconditions, abduction has been used to automate inference of invariants for program loops,<sup id="cite_ref-70" class="reference"><a href="#cite_note-70"><span class="cite-bracket">[</span>70<span class="cite-bracket">]</span></a></sup> inference of specifications of unknown code,<sup id="cite_ref-71" class="reference"><a href="#cite_note-71"><span class="cite-bracket">[</span>71<span class="cite-bracket">]</span></a></sup> and in synthesis of the programs themselves.<sup id="cite_ref-72" class="reference"><a href="#cite_note-72"><span class="cite-bracket">[</span>72<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=36" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239009302">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{clear:left;float:left;margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/18px-Socrates.png" decoding="async" width="18" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/27px-Socrates.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/36px-Socrates.png 2x" data-file-width="326" data-file-height="500" /></span></span></span><span class="portalbox-link"><a href="/wiki/Portal:Philosophy" title="Portal:Philosophy">Philosophy portal</a></span></li></ul> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col"> <ul><li><a href="/wiki/Argument" title="Argument">Argument</a> – Attempt to persuade or to determine the truth of a conclusion</li> <li><a href="/wiki/Argumentation_theory" title="Argumentation theory">Argumentation theory</a> – Academic field of logic and rhetoric</li> <li><a href="/wiki/Attribution_(psychology)" title="Attribution (psychology)">Attribution (psychology)</a> – The process by which individuals explain the causes of behavior and events</li> <li><a href="/wiki/Charles_Sanders_Peirce_bibliography" title="Charles Sanders Peirce bibliography">Charles Sanders Peirce bibliography</a></li> <li><a href="/wiki/Critical_thinking" title="Critical thinking">Critical thinking</a> – Analysis of facts to form a judgment</li> <li><a href="/wiki/Defeasible_reasoning" title="Defeasible reasoning">Defeasible reasoning</a> – Reasoning that is rationally compelling, though not deductively valid</li> <li><a href="/wiki/Douglas_N._Walton" title="Douglas N. Walton">Douglas N. Walton</a> – Canadian academic and author (1942–2020)</li> <li><a href="/wiki/Duck_test" title="Duck test">Duck test</a> – Classification based on observable evidence</li> <li><a href="/wiki/Falsifiability" title="Falsifiability">Falsifiability</a> – Property of a statement that can be logically contradicted</li> <li><a href="/wiki/Gregory_Bateson" title="Gregory Bateson">Gregory Bateson</a> – British-American psychological anthropologist (1904–1980)</li> <li><a href="/wiki/Heuristic" title="Heuristic">Heuristic</a> – Problem-solving method</li> <li><a href="/wiki/Inductive_probability" title="Inductive probability">Inductive probability</a> – Determining the probability of future events based on past events</li> <li><a href="/wiki/Illative_sense" title="Illative sense">Illative sense</a> – Epistemological concept</li> <li><a href="/wiki/Logical_reasoning" title="Logical reasoning">Logical reasoning</a> – Process of drawing correct inferences</li> <li><a href="/wiki/Maximum_likelihood_estimation" title="Maximum likelihood estimation">Maximum likelihood estimation</a> – Method of estimating the parameters of a statistical model, given observations</li> <li><a href="/wiki/Occam%27s_razor" title="Occam's razor">Occam's razor</a> – Philosophical problem-solving principle</li> <li><a href="/wiki/Sensemaking" title="Sensemaking">Sensemaking</a> – Giving meaning to collective experiences</li> <li><a href="/wiki/Sign_relation" title="Sign relation">Sign relation</a> – Concept in semiotics</li> <li><a href="/wiki/Statistical_model" title="Statistical model">Statistical model</a> – Type of mathematical model</li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=37" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-Josephson-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-Josephson_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Josephson_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">For example: <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFJosephsonJosephson1994" class="citation book cs1">Josephson, John R.; Josephson, Susan G., eds. (1994). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=uu6zXrogwWAC"><i>Abductive Inference: Computation, Philosophy, Technology</i></a>. Cambridge, UK; New York: Cambridge University Press. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FCBO9780511530128">10.1017/CBO9780511530128</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0521434614" title="Special:BookSources/978-0521434614"><bdi>978-0521434614</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/28149683">28149683</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Abductive+Inference%3A+Computation%2C+Philosophy%2C+Technology&rft.place=Cambridge%2C+UK%3B+New+York&rft.pub=Cambridge+University+Press&rft.date=1994&rft_id=info%3Aoclcnum%2F28149683&rft_id=info%3Adoi%2F10.1017%2FCBO9780511530128&rft.isbn=978-0521434614&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3Duu6zXrogwWAC&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140826115846/http://www.commens.org/dictionary/term/retroduction">"Retroduction"</a>. <i>Commens – Digital Companion to C. S. Peirce</i>. Mats Bergman, Sami Paavola & João Queiroz. Archived from <a rel="nofollow" class="external text" href="http://www.commens.org/dictionary/term/retroduction">the original</a> on August 26, 2014<span class="reference-accessdate">. Retrieved <span class="nowrap">August 24,</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Commens+%E2%80%93+Digital+Companion+to+C.+S.+Peirce&rft.atitle=Retroduction&rft_id=http%3A%2F%2Fwww.commens.org%2Fdictionary%2Fterm%2Fretroduction&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">See, e.g. <i>Analysis of Evidence, 2d ed.</i> by Terence Anderson (Cambridge University Press, 2005)</span> </li> <li id="cite_note-Josephson,_Magnani-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-Josephson,_Magnani_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Josephson,_Magnani_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">For examples, see "<a rel="nofollow" class="external text" href="https://web.archive.org/web/20110720020440/http://www.cse.ohio-state.edu/lair/Projects/Abduction/abduction.html">Abductive Inference in Reasoning and Perception</a>", John R. Josephson, Laboratory for Artificial Intelligence Research, Ohio State University, and <i>Abduction, Reason, and Science. Processes of Discovery and Explanation</i> by <a href="/wiki/Lorenzo_Magnani" title="Lorenzo Magnani">Lorenzo Magnani</a> (Kluwer Academic/Plenum Publishers, New York, 2001).</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFlachKakas2000" class="citation book cs1"><a href="/wiki/Peter_Flach" title="Peter Flach">Flach, P. A.</a>; Kakas, A. C., eds. (2000). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=E7fnCAAAQBAJ&pg=PA13"><i>Abduction and Induction: Essays on their Relation and Integration</i></a>. Springer. p. xiii<span class="reference-accessdate">. Retrieved <span class="nowrap">October 31,</span> 2016</span>. <q>This book grew out of a series of workshops on this topic. [Budapest 1996; Nagoya 1997; Brighton 1998]</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Abduction+and+Induction%3A+Essays+on+their+Relation+and+Integration&rft.pages=xiii&rft.pub=Springer&rft.date=2000&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DE7fnCAAAQBAJ%26pg%3DPA13&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">Reggia, James A., et al. "<a rel="nofollow" class="external text" href="http://www.cs.umd.edu/~nau/papers/reggia1985answer1.pdf">Answer justification in diagnostic expert systems-Part I: Abductive inference and its justification</a>." IEEE transactions on biomedical engineering 4 (1985): 263-267.</span> </li> <li id="cite_note-:0-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDouven2021" class="citation cs2">Douven, Igor (2021), <a rel="nofollow" class="external text" href="https://plato.stanford.edu/archives/sum2021/entries/abduction/">"Abduction"</a>, in Zalta, Edward N. (ed.), <i>The Stanford Encyclopedia of Philosophy</i> (Summer 2021 ed.), Metaphysics Research Lab, Stanford University<span class="reference-accessdate">, retrieved <span class="nowrap">April 17,</span> 2024</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Abduction&rft.btitle=The+Stanford+Encyclopedia+of+Philosophy&rft.edition=Summer+2021&rft.pub=Metaphysics+Research+Lab%2C+Stanford+University&rft.date=2021&rft.aulast=Douven&rft.aufirst=Igor&rft_id=https%3A%2F%2Fplato.stanford.edu%2Farchives%2Fsum2021%2Fentries%2Fabduction%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSober2013" class="citation book cs1"><a href="/wiki/Elliott_Sober" title="Elliott Sober">Sober, Elliott</a> (2013). <i>Core Questions in Philosophy: A Text with Readings</i> (6th ed.). Boston: Pearson Education. p. 28. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780205206698" title="Special:BookSources/9780205206698"><bdi>9780205206698</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/799024771">799024771</a>. <q>I now move to abduction—inference to the best explanation.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Core+Questions+in+Philosophy%3A+A+Text+with+Readings&rft.place=Boston&rft.pages=28&rft.edition=6th&rft.pub=Pearson+Education&rft.date=2013&rft_id=info%3Aoclcnum%2F799024771&rft.isbn=9780205206698&rft.aulast=Sober&rft.aufirst=Elliott&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCampos2011" class="citation journal cs1">Campos, Daniel G. (June 2011). "On the distinction between Peirce's abduction and Lipton's inference to the best explanation". <i><a href="/wiki/Synthese" title="Synthese">Synthese</a></i>. <b>180</b> (3): 419–442. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2Fs11229-009-9709-3">10.1007/s11229-009-9709-3</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:791688">791688</a>. <q>I argue against the tendency in the philosophy of science literature to link abduction to the inference to the best explanation (IBE), and in particular, to claim that Peircean abduction is a conceptual predecessor to IBE. [...] In particular, I claim that Peircean abduction is an in-depth account of the process of generating explanatory hypotheses, while IBE, at least in <a href="/wiki/Peter_Lipton" title="Peter Lipton">Peter Lipton</a>'s thorough treatment, is a more encompassing account of the processes both of generating and of evaluating scientific hypotheses. There is then a two-fold problem with the claim that abduction is IBE. On the one hand, it conflates abduction and induction, which are two distinct forms of logical inference, with two distinct aims, as shown by Charles S. Peirce; on the other hand it lacks a clear sense of the full scope of IBE as an account of scientific inference.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Synthese&rft.atitle=On+the+distinction+between+Peirce%27s+abduction+and+Lipton%27s+inference+to+the+best+explanation&rft.volume=180&rft.issue=3&rft.pages=419-442&rft.date=2011-06&rft_id=info%3Adoi%2F10.1007%2Fs11229-009-9709-3&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A791688%23id-name%3DS2CID&rft.aulast=Campos&rft.aufirst=Daniel+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWalton2001" class="citation journal cs1"><a href="/wiki/Douglas_N._Walton" title="Douglas N. Walton">Walton, Douglas</a> (2001). "Abductive, presumptive and plausible arguments". <i><a href="/wiki/Informal_Logic_(journal)" title="Informal Logic (journal)">Informal Logic</a></i>. <b>21</b> (2): 141–169. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.127.1593">10.1.1.127.1593</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.22329%2Fil.v21i2.2241">10.22329/il.v21i2.2241</a>. <q>Abductive inference has often been equated with inference to the best explanation. [...] The account of abductive inference and inference to the best explanation presented above has emphasized the common elements found in the analyses given by Peirce, Harman and the Josephsons. It is necessary to add that this brief account may be misleading in some respects, and that a closer and more detailed explication of the finer points of the three analyses could reveal important underlying philosophical differences. Inferences to the best explanation, as expounded by Harman and the Josephsons, can involve deductive and inductive processes of a kind that would be apparently be excluded by Peirce's account of abduction.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Informal+Logic&rft.atitle=Abductive%2C+presumptive+and+plausible+arguments&rft.volume=21&rft.issue=2&rft.pages=141-169&rft.date=2001&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.127.1593%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.22329%2Fil.v21i2.2241&rft.aulast=Walton&rft.aufirst=Douglas&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text">Cialdea Mayer, Marta and Pirri, Fiora (1993) "First order abduction via tableau and sequent calculi" Logic Jnl IGPL 1993 1: 99–117; <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fjigpal%2F1.1.99">10.1093/jigpal/1.1.99</a>. Oxford Journals</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text">Cialdea Mayer, Marta and Pirri, Fiora (1993) "Propositional abduction in modal logic" Logic Jnl IGPL 1995 3(6) 907–919; <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fjigpal%2F3.6.907">10.1093/jigpal/3.6.907</a>. Oxford Journals</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text">Peirce MS. 692, quoted in Sebeok, T. (1981) "<a rel="nofollow" class="external text" href="http://www.visual-memory.co.uk/b_resources/abduction.html">You Know My Method</a>" in Sebeok, T., <i>The Play of Musement</i>, Bloomington, IA: Indiana, page 24.</span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">Peirce MS. 696, quoted in Sebeok, T. (1981) "<a rel="nofollow" class="external text" href="http://www.visual-memory.co.uk/b_resources/abduction.html">You Know My Method</a>" in Sebeok, T., <i>The Play of Musement</i>, Bloomington, IA: Indiana, page 31.</span> </li> <li id="cite_note-Josang2016-SL-15"><span class="mw-cite-backlink">^ <a href="#cite_ref-Josang2016-SL_15-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Josang2016-SL_15-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">A. Jøsang. <i>Subjective Logic: A Formalism for Reasoning Under Uncertainty</i>, Springer 2016, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-319-42337-1" title="Special:BookSources/978-3-319-42337-1">978-3-319-42337-1</a></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPólya1945" class="citation book cs1">Pólya, George (1945). <i>How to solve it: a new aspect of mathematical method</i> (Expanded Princeton Science Library (2004) ed.). Princeton [N.J.]: Princeton University Press. p. 45. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-691-11966-X" title="Special:BookSources/0-691-11966-X"><bdi>0-691-11966-X</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=How+to+solve+it%3A+a+new+aspect+of+mathematical+method&rft.place=Princeton+%5BN.J.%5D&rft.pages=45&rft.edition=Expanded+Princeton+Science+Library+%282004%29&rft.pub=Princeton+University+Press&rft.date=1945&rft.isbn=0-691-11966-X&rft.aulast=P%C3%B3lya&rft.aufirst=George&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPopper2002" class="citation book cs1">Popper, Karl (2002). <i>Conjectures and Refutations: The Growth of Scientific Knowledge</i> (2 ed.). London: Routledge. p. 536.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Conjectures+and+Refutations%3A+The+Growth+of+Scientific+Knowledge&rft.place=London&rft.pages=536&rft.edition=2&rft.pub=Routledge&rft.date=2002&rft.aulast=Popper&rft.aufirst=Karl&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text">See Santaella, Lucia (1997) "The Development of Peirce's Three Types of Reasoning: Abduction, Deduction, and Induction", 6th Congress of the <a href="/wiki/IASS" class="mw-redirect" title="IASS">IASS</a>. <a rel="nofollow" class="external text" href="http://www.pucsp.br/~lbraga/epap_peir1.htm">Eprint</a>.</span> </li> <li id="cite_note-guess-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-guess_19-0">^</a></b></span> <span class="reference-text">Peirce, C. S. <ul><li>"On the Logic of drawing History from Ancient Documents especially from Testimonies" (1901), <i>Collected Papers</i> v. 7, paragraph 219.</li> <li>"PAP" ["Prolegomena to an Apology for Pragmatism"], MS 293 c. 1906, <i>New Elements of Mathematics</i> v. 4, pp. 319–320.</li> <li>A Letter to F. A. Woods (1913), <i>Collected Papers</i> v. 8, paragraphs 385–388.</li></ul> (See under "<a rel="nofollow" class="external text" href="http://www.helsinki.fi/science/commens/terms/abduction.html">Abduction</a>" and "<a rel="nofollow" class="external text" href="http://www.helsinki.fi/science/commens/terms/retroduction.html">Retroduction</a>" at <i>Commens Dictionary of Peirce's Terms</i>.)</span> </li> <li id="cite_note-HL-20"><span class="mw-cite-backlink">^ <a href="#cite_ref-HL_20-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-HL_20-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-HL_20-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-HL_20-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text">Peirce, C. S. (1903), Harvard lectures on pragmatism, <i>Collected Papers</i> v. 5, <a rel="nofollow" class="external text" href="http://www.textlog.de/7664-2.html">paragraphs 188–189</a>.</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text">Peirce, C. S. (1908), "<a href="https://en.wikisource.org/wiki/A_Neglected_Argument_for_the_Reality_of_God" class="extiw" title="s:A Neglected Argument for the Reality of God">A Neglected Argument for the Reality of God</a>", <i>Hibbert Journal</i> v. 7, pp. 90–112, see §4. In <i>Collected Papers</i> v. 6, see paragraph 476. In <i>The Essential Peirce</i> v. 2, see p. 444.</span> </li> <li id="cite_note-NA-22"><span class="mw-cite-backlink">^ <a href="#cite_ref-NA_22-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-NA_22-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-NA_22-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-NA_22-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text">Peirce, C. S. (1908), "<a href="https://en.wikisource.org/wiki/A_Neglected_Argument_for_the_Reality_of_God" class="extiw" title="s:A Neglected Argument for the Reality of God">A Neglected Argument for the Reality of God</a>", <i>Hibbert Journal</i> v. 7, pp. 90–112. See both part III and part IV. Reprinted, including originally unpublished portion, in <i>Collected Papers</i> v. 6, paragraphs 452–85, <i>Essential Peirce</i> v. 2, pp. 434–50, and elsewhere.</span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text">Peirce used the term "intuition" not in the sense of an instinctive or anyway half-conscious inference as people often do currently. Instead he used "intuition" usually in the sense of a cognition devoid of logical determination by <a href="/wiki/A_priori_and_a_posteriori" title="A priori and a posteriori">previous cognitions</a>. He said, "We have no power of Intuition" in that sense. See his "Some Consequences of Four Incapacities" (1868), <a rel="nofollow" class="external text" href="http://www.peirce.org/writings/p27.html">Eprint</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110514094121/http://www.peirce.org/writings/p27.html">Archived</a> 2011-05-14 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text">For a relevant discussion of Peirce and the aims of abductive inference, see McKaughan, Daniel J. (2008), "<a rel="nofollow" class="external text" href="https://muse.jhu.edu/article/252833/summary">From Ugly Duckling to Swan: C. S. Peirce, Abduction, and the Pursuit of Scientific Theories</a>", <i>Transactions of the Charles S. Peirce Society</i>, v. 44, no. 3 (summer), 446–468.</span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-25">^</a></b></span> <span class="reference-text">Peirce means "conceivable" very broadly. See <i>Collected Papers</i> v. 5, paragraph 196, or <i>Essential Peirce</i> v. 2, p. 235, "Pragmatism as the Logic of Abduction" (Lecture VII of the 1903 Harvard lectures on pragmatism): <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>It allows any flight of imagination, provided this imagination ultimately alights upon a possible practical effect; and thus many hypotheses may seem at first glance to be excluded by the pragmatical maxim that are not really so excluded.</p></blockquote></span> </li> <li id="cite_note-L75-26"><span class="mw-cite-backlink">^ <a href="#cite_ref-L75_26-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-L75_26-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-L75_26-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-L75_26-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text">Peirce, C. S., Carnegie Application (L75, 1902, <i>New Elements of Mathematics</i> v. 4, pp. 37–38. See under "<a rel="nofollow" class="external text" href="http://www.helsinki.fi/science/commens/terms/abduction.html">Abduction</a>" at the <i>Commens Dictionary of Peirce's Terms</i>: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>Methodeutic has a special interest in Abduction, or the inference which starts a scientific hypothesis. For it is not sufficient that a hypothesis should be a justifiable one. Any hypothesis which explains the facts is justified critically. But among justifiable hypotheses we have to select that one which is suitable for being tested by experiment.</p></blockquote></span> </li> <li id="cite_note-prag-27"><span class="mw-cite-backlink">^ <a href="#cite_ref-prag_27-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-prag_27-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-prag_27-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-prag_27-3"><sup><i><b>d</b></i></sup></a></span> <span class="reference-text">Peirce, "Pragmatism as the Logic of Abduction" (Lecture VII of the 1903 Harvard lectures on pragmatism), see parts III and IV. Published in part in <i>Collected Papers</i> v. 5, paragraphs 180–212 (see 196–200, <a rel="nofollow" class="external text" href="http://www.textlog.de/7663.html">Eprint</a> and in full in <i>Essential Peirce</i> v. 2, pp. 226–241 (see sections III and IV). <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>.... What is good abduction? What should an explanatory hypothesis be to be worthy to rank as a hypothesis? Of course, it must explain the facts. But what other conditions ought it to fulfill to be good? .... Any hypothesis, therefore, may be admissible, in the absence of any special reasons to the contrary, provided it be capable of experimental verification, and only insofar as it is capable of such verification. This is approximately the doctrine of pragmatism.</p></blockquote></span> </li> <li id="cite_note-econ-28"><span class="mw-cite-backlink">^ <a href="#cite_ref-econ_28-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-econ_28-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-econ_28-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">Peirce, C.S. (1902), application to the Carnegie Institution, see MS L75.329-330, from <a rel="nofollow" class="external text" href="http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-08.htm#m27">Draft D</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110524021101/http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-08.htm#m27">Archived</a> 2011-05-24 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> of Memoir 27: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>Consequently, to discover is simply to expedite an event that would occur sooner or later, if we had not troubled ourselves to make the discovery. Consequently, the art of discovery is purely a question of economics. The economics of research is, so far as logic is concerned, the leading doctrine with reference to the art of discovery. Consequently, the conduct of abduction, which is chiefly a question of <a href="/wiki/Heuristic" title="Heuristic">heuristic</a> and is the first question of heuristic, is to be governed by economical considerations.</p></blockquote></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text">Peirce, A Letter to <a href="/wiki/Paul_Carus" title="Paul Carus">Paul Carus</a> circa 1910, <i>Collected Papers</i> v. 8, paragraphs 227–228. See under "<a rel="nofollow" class="external text" href="http://www.helsinki.fi/science/commens/terms/hypothesis.html">Hypothesis</a>" at the <i>Commens Dictionary of Peirce's Terms</i>.</span> </li> <li id="cite_note-NCA-30"><span class="mw-cite-backlink">^ <a href="#cite_ref-NCA_30-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-NCA_30-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">(1867), "On the Natural Classification of Arguments", <i>Proceedings of the American Academy of Arts and Sciences</i> v. 7, pp. 261–287. Presented April 9, 1867. See especially starting at <a rel="nofollow" class="external text" href="https://books.google.com/books?id=nG8UAAAAYAAJ&pg=PA284">p. 284</a> in Part III §1. Reprinted in <i>Collected Papers v. 2, paragraphs 461–516 and </i>Writings<i> v. 2, pp. 23–49.</i></span> </li> <li id="cite_note-DIH-31"><span class="mw-cite-backlink">^ <a href="#cite_ref-DIH_31-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-DIH_31-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-DIH_31-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text">Peirce, C. S. (1878), "Deduction, Induction, and Hypothesis", <i>Popular Science Monthly</i>, v. 13, pp. 470–82, see <a rel="nofollow" class="external text" href="https://books.google.com/books?id=u8sWAQAAIAAJ&pg=PA472">472</a>. <i>Collected Papers</i> 2.619–44, see 623.</span> </li> <li id="cite_note-L2L-32"><span class="mw-cite-backlink">^ <a href="#cite_ref-L2L_32-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-L2L_32-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">A letter to Langley, 1900, published in <i>Historical Perspectives on Peirce's Logic of Science</i>. See excerpts under "<a rel="nofollow" class="external text" href="http://www.helsinki.fi/science/commens/terms/abduction.html">Abduction</a>" at the <i>Commens Dictionary of Peirce's Terms</i>.</span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text">"A Syllabus of Certain Topics of Logic'" (1903 manuscript), <i>Essential Peirce</i> v. 2, see p. 287. See under "<a rel="nofollow" class="external text" href="http://www.helsinki.fi/science/commens/terms/abduction.html">Abduction</a>" at the <i>Commens Dictionary of Peirce's Terms</i>.</span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text">Peirce, C. S., "On the Logic of Drawing History from Ancient Documents", dated as <i>circa</i> 1901 both by the editors of <i>Collected Papers</i> (see CP v. 7, bk 2, ch. 3, footnote 1) and by those of the <i>Essential Peirce</i> (EP) (<a rel="nofollow" class="external text" href="http://www.iupui.edu/~peirce/ep/ep2/headers/ep2headx.htm#8">Eprint</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120905022758/http://www.iupui.edu/~peirce/ep/ep2/headers/ep2headx.htm#8">Archived</a> 2012-09-05 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>. The article's discussion of abduction is in CP v. 7, paragraphs 218–31 and in EP v. 2, pp. 107–14.</span> </li> <li id="cite_note-newidea-35"><span class="mw-cite-backlink">^ <a href="#cite_ref-newidea_35-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-newidea_35-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Peirce, C. S., "A Syllabus of Certain Topics of Logic" (1903), <i>Essential Peirce</i> v. 2, p. 287: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p> The mind seeks to bring the facts, as modified by the new discovery, into order; that is, to form a general conception embracing them. In some cases, it does this by an act of <i>generalization</i>. In other cases, no new law is suggested, but only a peculiar state of facts that will "explain" the surprising phenomenon; and a law already known is recognized as applicable to the suggested hypothesis, so that the phenomenon, under that assumption, would not be surprising, but quite likely, or even would be a necessary result. This synthesis suggesting a new conception or hypothesis, is the Abduction.</p></blockquote></span> </li> <li id="cite_note-kehler-36"><span class="mw-cite-backlink">^ <a href="#cite_ref-kehler_36-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-kehler_36-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">A Letter to J. H. Kehler (1911), <i>New Elements of Mathematics</i> v. 3, pp. 203–4, see under "<a rel="nofollow" class="external text" href="http://www.helsinki.fi/science/commens/terms/retroduction.html">Retroduction</a>" at <i>Commens Dictionary of Peirce's Terms</i>.</span> </li> <li id="cite_note-Pierce-1883-37"><span class="mw-cite-backlink"><b><a href="#cite_ref-Pierce-1883_37-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPeirce1883" class="citation book cs1">Peirce, Charles S. (1883). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190308080846/http://www.commens.org/bibliography/collection_article/peirce-charles-s-1883-theory-probable-inference-studies-logic">"A theory of probable inference"</a>. In Peirce, Charles S. (ed.). <a href="/wiki/Charles_Sanders_Peirce_bibliography#SIL" title="Charles Sanders Peirce bibliography"><i>Studies in Logic by Members of the Johns Hopkins University</i></a>. Boston, MA: Little, Brown, and Company. Archived from <a rel="nofollow" class="external text" href="http://www.commens.org/bibliography/collection_article/peirce-charles-s-1883-theory-probable-inference-studies-logic">the original</a> on March 8, 2019<span class="reference-accessdate">. Retrieved <span class="nowrap">March 7,</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=A+theory+of+probable+inference&rft.btitle=Studies+in+Logic+by+Members+of+the+Johns+Hopkins+University&rft.place=Boston%2C+MA&rft.pub=Little%2C+Brown%2C+and+Company&rft.date=1883&rft.aulast=Peirce&rft.aufirst=Charles+S.&rft_id=http%3A%2F%2Fwww.commens.org%2Fbibliography%2Fcollection_article%2Fpeirce-charles-s-1883-theory-probable-inference-studies-logic&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-38"><span class="mw-cite-backlink"><b><a href="#cite_ref-38">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSebeokUmiker-Sebeok1979" class="citation journal cs1"><a href="/wiki/Thomas_Sebeok" title="Thomas Sebeok">Sebeok, Thomas A.</a>; Umiker-Sebeok, Jean (1979). "<span class="cs1-kern-left"></span>'You know my method': A juxtaposition of Charles S. Peirce and Sherlock Holmes". <i><a href="/wiki/Semiotica" title="Semiotica">Semiotica</a></i>. <b>26</b> (3–4): 203–250. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1515%2Fsemi.1979.26.3-4.203">10.1515/semi.1979.26.3-4.203</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:170683439">170683439</a>. <q><a href="/wiki/Marcello_Truzzi" title="Marcello Truzzi">Marcello Truzzi</a>, in a searching article on Holmes's method (1973:93–126), anticipated our present work by pointing to the similarities between the detective's so-called deductions, or inductions, and Peirce's abductions, or conjectures. According to Peirce's system of logic, furthermore, Holmes's observations are themselves a form of abduction, and abduction is as legitimate a type of logical inference as either induction or deduction (Peirce 8.228).</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Semiotica&rft.atitle=%27You+know+my+method%27%3A+A+juxtaposition+of+Charles+S.+Peirce+and+Sherlock+Holmes&rft.volume=26&rft.issue=3%E2%80%934&rft.pages=203-250&rft.date=1979&rft_id=info%3Adoi%2F10.1515%2Fsemi.1979.26.3-4.203&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A170683439%23id-name%3DS2CID&rft.aulast=Sebeok&rft.aufirst=Thomas+A.&rft.au=Umiker-Sebeok%2C+Jean&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-39"><span class="mw-cite-backlink"><b><a href="#cite_ref-39">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNiiniluoto1999" class="citation journal cs1"><a href="/wiki/Ilkka_Niiniluoto" title="Ilkka Niiniluoto">Niiniluoto, Ilkka</a> (September 1999). "Defending abduction". <i><a href="/wiki/Philosophy_of_Science_(journal)" title="Philosophy of Science (journal)">Philosophy of Science</a></i>. <b>66</b> (Supplement 1): S436–S451 (S440–S441). <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1086%2F392744">10.1086/392744</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:224841752">224841752</a>. <q>A historically interesting application of abduction as a heuristic method can be found in classical detective stories, as shown by the semiotical and logical essays collected in Eco and Sebeok 1983. <a href="/wiki/C._Auguste_Dupin" title="C. Auguste Dupin">C. Auguste Dupin</a>, the hero of <a href="/wiki/Edgar_Allan_Poe" title="Edgar Allan Poe">Edgar Allan Poe</a>'s novels in the 1840s, employed a method of 'ratiocination' or 'analysis' which has the structure of retroduction. Similarly, the logic of the 'deductions' of Sherlock Holmes is typically abductive.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophy+of+Science&rft.atitle=Defending+abduction&rft.volume=66&rft.issue=Supplement+1&rft.pages=S436-S451+%28S440-S441%29&rft.date=1999-09&rft_id=info%3Adoi%2F10.1086%2F392744&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A224841752%23id-name%3DS2CID&rft.aulast=Niiniluoto&rft.aufirst=Ilkka&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-40"><span class="mw-cite-backlink"><b><a href="#cite_ref-40">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCarson2009" class="citation journal cs1">Carson, David (June 2009). <a rel="nofollow" class="external text" href="https://researchportal.port.ac.uk/ws/files/84295/ijps.2009.11.2.pdf">"The abduction of Sherlock Holmes"</a> <span class="cs1-format">(PDF)</span>. <i>International Journal of Police Science & Management</i>. <b>11</b> (2): 193–202. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1350%2Fijps.2009.11.2.123">10.1350/ijps.2009.11.2.123</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:145337828">145337828</a>. <q>Sherlock Holmes, although a fictional character, remains renowned as a great detective. However, his methodology, which was <i>abduction</i> rather than deduction, and which is innocently used by many real detectives, is rarely described, discussed, or researched. This paper compares and contrasts the three forms of inferential reasoning, and makes a case for articulating and developing the role of abduction in the work, and training, of police officers.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Police+Science+%26+Management&rft.atitle=The+abduction+of+Sherlock+Holmes&rft.volume=11&rft.issue=2&rft.pages=193-202&rft.date=2009-06&rft_id=info%3Adoi%2F10.1350%2Fijps.2009.11.2.123&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A145337828%23id-name%3DS2CID&rft.aulast=Carson&rft.aufirst=David&rft_id=https%3A%2F%2Fresearchportal.port.ac.uk%2Fws%2Ffiles%2F84295%2Fijps.2009.11.2.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-41"><span class="mw-cite-backlink"><b><a href="#cite_ref-41">^</a></b></span> <span class="reference-text">In Peirce, C. S., 'Minute Logic' circa 1902, <i>Collected Papers</i> v. 2, paragraph 102. See under "<a rel="nofollow" class="external text" href="http://www.helsinki.fi/science/commens/terms/abduction.html">Abduction</a>" at <i>Commens Dictionary of Peirce's Terms</i>.</span> </li> <li id="cite_note-42"><span class="mw-cite-backlink"><b><a href="#cite_ref-42">^</a></b></span> <span class="reference-text">Peirce, "On the Logic of drawing History from Ancient Documents", 1901 manuscript, <i>Collected Papers</i> v. 7, paragraphs 164–231, see 202, reprinted in <i>Essential Peirce</i> v. 2, pp. 75–114, see 95. See under "<a rel="nofollow" class="external text" href="http://www.helsinki.fi/science/commens/terms/abduction.html">Abduction</a>" at <i>Commens Dictionary of Peirce's Terms</i>.</span> </li> <li id="cite_note-43"><span class="mw-cite-backlink"><b><a href="#cite_ref-43">^</a></b></span> <span class="reference-text">Peirce, "On the Logic of Drawing Ancient History from Documents", <i>Essential Peirce</i> v. 2, see pp. 107–9.</span> </li> <li id="cite_note-44"><span class="mw-cite-backlink"><b><a href="#cite_ref-44">^</a></b></span> <span class="reference-text">Peirce, Carnegie application, L75 (1902), Memoir 28: "On the Economics of Research", scroll down to Draft E. <a rel="nofollow" class="external text" href="http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-08.htm#m28">Eprint</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110524021101/http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-08.htm#m28">Archived</a> 2011-05-24 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>.</span> </li> <li id="cite_note-45"><span class="mw-cite-backlink"><b><a href="#cite_ref-45">^</a></b></span> <span class="reference-text">Peirce, C. S., the 1866 Lowell Lectures on the Logic of Science, <i><a href="/wiki/Charles_Sanders_Peirce_bibliography#W" title="Charles Sanders Peirce bibliography">Writings of Charles S. Peirce</a></i> v. 1, p. 485. See under "<a rel="nofollow" class="external text" href="http://www.helsinki.fi/science/commens/terms/hypothesis.html">Hypothesis</a>" at <i>Commens Dictionary of Peirce's Terms</i>.</span> </li> <li id="cite_note-46"><span class="mw-cite-backlink"><b><a href="#cite_ref-46">^</a></b></span> <span class="reference-text">Peirce, C. S., "A Syllabus of Certain Topics of Logic", written 1903. See <i><a href="/wiki/Charles_Sanders_Peirce_bibliography#EP" title="Charles Sanders Peirce bibliography">The Essential Peirce</a></i> v. 2, p. 287. Quote viewable under "<a rel="nofollow" class="external text" href="http://www.helsinki.fi/science/commens/terms/abduction.html">Abduction</a>" at <i>Commens Dictionary of Peirce's Terms</i>.</span> </li> <li id="cite_note-47"><span class="mw-cite-backlink"><b><a href="#cite_ref-47">^</a></b></span> <span class="reference-text">Peirce, A Letter to Paul Carus 1910, <i>Collected Papers</i> v. 8, see paragraph 223.</span> </li> <li id="cite_note-48"><span class="mw-cite-backlink"><b><a href="#cite_ref-48">^</a></b></span> <span class="reference-text">Peirce, C. S. (1902), Application to the Carnegie Institution, Memoir 27, <a rel="nofollow" class="external text" href="http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-08.htm#m27">Eprint</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20110524021101/http://www.cspeirce.com/menu/library/bycsp/l75/ver1/l75v1-08.htm#m27">Archived</a> 2011-05-24 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a>: "Of the different classes of arguments, abductions are the only ones in which after they have been admitted to be just, it still remains to inquire whether they are advantageous."</span> </li> <li id="cite_note-econ2-49"><span class="mw-cite-backlink"><b><a href="#cite_ref-econ2_49-0">^</a></b></span> <span class="reference-text">Peirce, "On the Logic of Drawing Ancient History from Documents", <i>Essential Peirce</i> v. 2, see pp. 107–9 and 113. On Twenty Questions, p. 109, Peirce has pointed out that if each question eliminates half the possibilities, twenty questions can choose from among 2<sup>20</sup> or 1,048,576 objects, and goes on to say: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1244412712"><blockquote class="templatequote"><p>Thus, twenty skillful hypotheses will ascertain what 200,000 stupid ones might fail to do. The secret of the business lies in the caution which breaks a hypothesis up into its smallest logical components, and only risks one of them at a time.</p></blockquote></span> </li> <li id="cite_note-50"><span class="mw-cite-backlink"><b><a href="#cite_ref-50">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140826222027/http://www.commens.org/">"An Essay toward Improving Our Reasoning in Security and in Uberty"</a>. <i>www.commens.org</i>. Archived from <a rel="nofollow" class="external text" href="http://www.commens.org/">the original</a> on August 26, 2014<span class="reference-accessdate">. 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Abductive planning with the event calculus. In Robert A. Kowalski, Kenneth A. Bowen editors: Logic Programming, Proceedings of the Fifth International Conference and Symposium, Seattle, Washington, August 15–19, 1988. MIT Press 1988, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-262-61056-6" title="Special:BookSources/0-262-61056-6">0-262-61056-6</a></span> </li> <li id="cite_note-Gärdenfors-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-Gärdenfors_58-0">^</a></b></span> <span class="reference-text">Gärdenfors, Peter. "Belief revision: A vade-mecum." Meta-Programming in Logic: Third International Workshop, META-92 Uppsala, Sweden, June 10–12, 1992 Proceedings 3. 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Cambridge: Cambridge University Press. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-44665-1" title="Special:BookSources/0-521-44665-1">0-521-44665-1</a></span> </li> <li id="cite_note-61"><span class="mw-cite-backlink"><b><a href="#cite_ref-61">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRose,_McKinley,_&_Briggs_Baffoe-Djan2020" class="citation book cs1">Rose, McKinley, & Briggs Baffoe-Djan (2020). <i>Data Collection Research Methods in Applied Linguistics</i>. Bloomsbury. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781350025851" title="Special:BookSources/9781350025851"><bdi>9781350025851</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Data+Collection+Research+Methods+in+Applied+Linguistics&rft.pub=Bloomsbury&rft.date=2020&rft.isbn=9781350025851&rft.au=Rose%2C+McKinley%2C+%26+Briggs+Baffoe-Djan&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span><span class="cs1-maint citation-comment"><code class="cs1-code">{{<a href="/wiki/Template:Cite_book" title="Template:Cite book">cite book</a>}}</code>: CS1 maint: multiple names: authors list (<a href="/wiki/Category:CS1_maint:_multiple_names:_authors_list" title="Category:CS1 maint: multiple names: authors list">link</a>)</span></span> </li> <li id="cite_note-62"><span class="mw-cite-backlink"><b><a href="#cite_ref-62">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMcKinley2019" class="citation book cs1">McKinley, J (December 6, 2019). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20200215113328/https://www.englishappliedlinguistics.com/uploads/2/4/1/9/2419477/mckinley__2020__theorizing_applied_linguistics_research.pdf">"Introduction: Theorizing research methods in the 'golden age' of applied linguistics research"</a> <span class="cs1-format">(PDF)</span>. In McKinley & Rose (ed.). <i>The Routledge Handbook of Research Methods in Applied Linguistics</i>. Abingdon: Routledge. pp. 1–13. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780367824471" title="Special:BookSources/9780367824471"><bdi>9780367824471</bdi></a>. Archived from <a rel="nofollow" class="external text" href="https://www.englishappliedlinguistics.com/uploads/2/4/1/9/2419477/mckinley__2020__theorizing_applied_linguistics_research.pdf">the original</a> <span class="cs1-format">(PDF)</span> on February 15, 2020<span class="reference-accessdate">. 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Indiana University Press. p. 131. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780253359551" title="Special:BookSources/9780253359551"><bdi>9780253359551</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Theory+of+Semiotics&rft.pages=131&rft.pub=Indiana+University+Press&rft.date=1976&rft.isbn=9780253359551&rft.aulast=Eco&rft.aufirst=Umberto&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DBoXO4ItsuaMC%26pg%3DPA131&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></span> </li> <li id="cite_note-Gell,_A_1984,_p_14-64"><span class="mw-cite-backlink">^ <a href="#cite_ref-Gell,_A_1984,_p_14_64-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Gell,_A_1984,_p_14_64-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGell1998" class="citation book cs1">Gell, A. 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Peirce Society</i>, v. 44, no. 3 (summer), 446–468.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMenzies1996" class="citation journal cs1">Menzies, T (1996). <a rel="nofollow" class="external text" href="http://menzies.us/pdf/96abkl.pdf">"Applications of Abduction: Knowledge-Level Modeling"</a> <span class="cs1-format">(PDF)</span>. <i>International Journal of Human-Computer Studies</i>. <b>45</b> (3): 305–335. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.352.8159">10.1.1.352.8159</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1006%2Fijhc.1996.0054">10.1006/ijhc.1996.0054</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=International+Journal+of+Human-Computer+Studies&rft.atitle=Applications+of+Abduction%3A+Knowledge-Level+Modeling&rft.volume=45&rft.issue=3&rft.pages=305-335&rft.date=1996&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.352.8159%23id-name%3DCiteSeerX&rft_id=info%3Adoi%2F10.1006%2Fijhc.1996.0054&rft.aulast=Menzies&rft.aufirst=T&rft_id=http%3A%2F%2Fmenzies.us%2Fpdf%2F96abkl.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></li> <li>Queiroz, Joao & Merrell, Floyd (guest eds.). (2005). "Abduction - between subjectivity and objectivity". (special issue on abductive inference) <i><a href="/wiki/Semiotica" title="Semiotica">Semiotica</a></i> 153 (1/4). <a rel="nofollow" class="external autonumber" href="http://www.degruyter.com/view/j/semi.2005.2005.issue-153-1-4/issue-files/semi.2005.2005.issue-153-1-4.xml">[1]</a>.</li> <li>Santaella, Lucia (1997) "The Development of Peirce's Three Types of Reasoning: Abduction, Deduction, and Induction", 6th Congress of the <a href="/wiki/IASS" class="mw-redirect" title="IASS">IASS</a>. <a rel="nofollow" class="external text" href="http://www.pucsp.br/~lbraga/epap_peir1.htm">Eprint</a>.</li> <li>Sebeok, T. (1981) "You Know My Method". In Sebeok, T. "The Play of Musement". Indiana. Bloomington, IA.</li> <li>Yu, Chong Ho (1994), "Is There a Logic of Exploratory Data Analysis?", <i>Annual Meeting of American Educational Research Association</i>, New Orleans, LA, April, 1994. <a rel="nofollow" class="external text" href="http://www.creative-wisdom.com/pub/Peirce/Logic_of_EDA.html">Website of Dr. Chong Ho (Alex) Yu</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Abductive_reasoning&action=edit&section=39" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/abductive_reasoning" class="extiw" title="wiktionary:abductive reasoning">abductive reasoning</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1235681985"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237033735"><div class="side-box side-box-right plainlinks sistersitebox"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1126788409"> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/40px-Wiktionary-logo-en-v2.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/60px-Wiktionary-logo-en-v2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Wiktionary-logo-en-v2.svg/80px-Wiktionary-logo-en-v2.svg.png 2x" data-file-width="512" data-file-height="512" /></span></span></div> <div class="side-box-text plainlist">Look up <i><b><a href="https://en.wiktionary.org/wiki/abductive" class="extiw" title="wiktionary:abductive">abductive</a></b></i> or <i><b><a href="https://en.wiktionary.org/wiki/abductive_reasoning" class="extiw" title="wiktionary:abductive reasoning">abductive reasoning</a></b></i> in Wiktionary, the free dictionary.</div></div> </div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDouven" class="citation encyclopaedia cs1">Douven, Igor. <a rel="nofollow" class="external text" href="https://plato.stanford.edu/entries/abduction/">"Abduction"</a>. In <a href="/wiki/Edward_N._Zalta" title="Edward N. Zalta">Zalta, Edward N.</a> (ed.). <i><a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Abduction&rft.btitle=Stanford+Encyclopedia+of+Philosophy&rft.aulast=Douven&rft.aufirst=Igor&rft_id=https%3A%2F%2Fplato.stanford.edu%2Fentries%2Fabduction%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AAbductive+reasoning" class="Z3988"></span></li> <li><a rel="nofollow" class="external text" href="https://www.inphoproject.org/idea/5421">Abductive reasoning</a> at the <a href="/wiki/Indiana_Philosophy_Ontology_Project" class="mw-redirect" title="Indiana Philosophy Ontology Project">Indiana Philosophy Ontology Project</a></li> <li><a rel="nofollow" class="external text" href="https://philpapers.org/browse/inference-to-the-best-explanation">Abductive reasoning</a> at <a href="/wiki/PhilPapers" title="PhilPapers">PhilPapers</a></li> <li>"<a rel="nofollow" class="external text" href="https://web.archive.org/web/20131214005416/http://www.cse.ohio-state.edu/lair/research.html">Abductive Inference</a>" (once there, scroll down), John R. Josephson, Laboratory for Artificial Intelligence Research, Ohio State University. (<a rel="nofollow" class="external text" href="https://web.archive.org/web/20110720020440/http://www.cse.ohio-state.edu/lair/Projects/Abduction/abduction.html">Former webpage</a> via the Wayback Machine.)</li> <li>"<a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/peirce/#dia">Deduction, Induction, and Abduction</a>", Chapter 3 in article "<a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/peirce/">Charles Sanders Peirce</a>" by <a href="/wiki/Robert_W._Burch" title="Robert W. Burch">Robert W. Burch</a>, 2001 and 2006, in the <a rel="nofollow" class="external text" href="http://plato.stanford.edu/">Stanford Encyclopedia of Philosophy</a>.</li> <li>"<a rel="nofollow" class="external text" href="https://web.archive.org/web/20100609064615/http://carbon.ucdenver.edu/~mryder/itc/abduction.html">Abduction</a>", links to articles and websites on abductive inference, <a rel="nofollow" class="external text" href="https://web.archive.org/web/20100914010915/http://carbon.ucdenver.edu/~mryder/martin.html">Martin Ryder</a>.</li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20091028001425/http://user.uni-frankfurt.de/~wirth/">International Research Group on Abductive Inference</a>, Uwe Wirth and Alexander Roesler, eds. Uses frames. Click on link at bottom of its home page for English. Wirth moved to <a href="/wiki/University_of_Gie%C3%9Fen" class="mw-redirect" title="University of Gießen">U. of Gießen</a>, Germany, and set up <a rel="nofollow" class="external text" href="https://archive.today/20130210054159/http://www.abduktionsforschung.de/">Abduktionsforschung</a>, home page not in English but see Artikel section there. <a rel="nofollow" class="external text" href="https://translate.google.com/translate?js=n&layout=2&eotf=1&sl=de&tl=en&u=http%3A%2F%2Fwww.abduktionsforschung.de%2Fabduktionsforschung.html">Abduktionsforschung home page via Google translation</a>.</li> <li>"<a rel="nofollow" class="external text" href="http://www.visual-memory.co.uk/b_resources/abduction.html">'You Know My Method': A Juxtaposition of Charles S. Peirce and Sherlock Holmes</a>" (1981), by <a href="/wiki/Thomas_Sebeok" title="Thomas Sebeok">Thomas Sebeok</a> with Jean Umiker-Sebeok, from <i>The Play of Musement</i>, Thomas Sebeok, Bloomington, Indiana: Indiana University Press, pp. 17–52.</li> <li><a rel="nofollow" class="external text" href="http://www.helsinki.fi/science/commens/dictionary.html">Commens Dictionary of Peirce's Terms</a>, Mats Bergman and Sami Paavola, editors, Helsinki U. Peirce's own definitions, often many per term across the decades. There, see "Hypothesis [as a form of reasoning]", "Abduction", "Retroduction", and "Presumption [as a form of reasoning]".</li> <li><a rel="nofollow" class="external text" href="https://philsci-archive.pitt.edu/22699/">"Touching Reality"</a>, a critique of abductive reasoning in the context of cosmology.</li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output 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title="Logic">Logic</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Outline_of_logic" title="Outline of logic">Outline</a></li> <li><a href="/wiki/History_of_logic" title="History of logic">History</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Major fields</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Logic_in_computer_science" title="Logic in computer science">Computer science</a></li> <li><a href="/wiki/Formal_semantics_(natural_language)" title="Formal semantics (natural language)">Formal semantics (natural language)</a></li> <li><a href="/wiki/Inference" title="Inference">Inference</a></li> <li><a href="/wiki/Philosophy_of_logic" title="Philosophy of logic">Philosophy of logic</a></li> <li><a href="/wiki/Formal_proof" title="Formal proof">Proof</a></li> <li><a href="/wiki/Semantics_of_logic" title="Semantics of logic">Semantics of logic</a></li> <li><a href="/wiki/Syntax_(logic)" title="Syntax (logic)">Syntax</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Logics</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Classical_logic" title="Classical logic">Classical</a></li> <li><a href="/wiki/Informal_logic" title="Informal logic">Informal</a> <ul><li><a href="/wiki/Critical_thinking" title="Critical thinking">Critical thinking</a></li> <li><a href="/wiki/Reason" title="Reason">Reason</a></li></ul></li> <li><a href="/wiki/Mathematical_logic" title="Mathematical logic">Mathematical</a></li> <li><a href="/wiki/Non-classical_logic" title="Non-classical logic">Non-classical</a></li> <li><a href="/wiki/Philosophical_logic" title="Philosophical logic">Philosophical</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theories</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Argumentation_theory" title="Argumentation theory">Argumentation</a></li> <li><a href="/wiki/Metalogic" title="Metalogic">Metalogic</a></li> <li><a href="/wiki/Metamathematics" title="Metamathematics">Metamathematics</a></li> <li><a href="/wiki/Set_theory" title="Set theory">Set</a></li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Foundations</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Abduction</a></li> <li><a href="/wiki/Analytic%E2%80%93synthetic_distinction" title="Analytic–synthetic distinction">Analytic and synthetic propositions</a></li> <li><a href="/wiki/Antecedent_(logic)" title="Antecedent (logic)">Antecedent</a></li> <li><a href="/wiki/Consequent" title="Consequent">Consequent</a></li> <li><a href="/wiki/Contradiction" title="Contradiction">Contradiction</a> <ul><li><a href="/wiki/Paradox" title="Paradox">Paradox</a></li> <li><a href="/wiki/Antinomy" title="Antinomy">Antinomy</a></li></ul></li> <li><a href="/wiki/Deductive_reasoning" title="Deductive reasoning">Deduction</a></li> <li><a href="/wiki/Deductive_closure" title="Deductive closure">Deductive closure</a></li> <li><a href="/wiki/Definition" title="Definition">Definition</a></li> <li><a href="/wiki/Description" title="Description">Description</a></li> <li><a href="/wiki/Logical_consequence" title="Logical consequence">Entailment</a> <ul><li><a href="/wiki/Entailment_(linguistics)" title="Entailment (linguistics)">Linguistic</a></li></ul></li> <li><a href="/wiki/Logical_form" title="Logical form">Form</a></li> <li><a href="/wiki/Inductive_reasoning" title="Inductive reasoning">Induction</a></li> <li><a href="/wiki/Logical_truth" title="Logical truth">Logical truth</a></li> <li><a href="/wiki/Name" title="Name">Name</a></li> <li><a href="/wiki/Necessity_and_sufficiency" title="Necessity and sufficiency">Necessity and sufficiency</a></li> <li><a href="/wiki/Premise" title="Premise">Premise</a></li> <li><a href="/wiki/Probability" title="Probability">Probability</a></li> <li><a href="/wiki/Proposition" title="Proposition">Proposition</a></li> <li><a href="/wiki/Reference" title="Reference">Reference</a></li> <li><a href="/wiki/Statement_(logic)" title="Statement (logic)">Statement</a></li> <li><a href="/wiki/Substitution_(logic)" title="Substitution (logic)">Substitution</a></li> <li><a href="/wiki/Truth" title="Truth">Truth</a></li> <li><a href="/wiki/Validity_(logic)" title="Validity (logic)">Validity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Lists</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;"><a href="/wiki/Index_of_logic_articles" title="Index of logic articles">topics</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_mathematical_logic_topics" title="List of mathematical logic topics">Mathematical logic</a></li> <li><a href="/wiki/List_of_Boolean_algebra_topics" title="List of Boolean algebra topics">Boolean algebra</a></li> <li><a href="/wiki/List_of_set_theory_topics" title="List of set theory topics">Set theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;font-weight:normal;">other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/List_of_logicians" title="List of logicians">Logicians</a></li> <li><a href="/wiki/List_of_rules_of_inference" title="List of rules of inference">Rules of inference</a></li> <li><a href="/wiki/List_of_paradoxes" title="List of paradoxes">Paradoxes</a></li> <li><a href="/wiki/List_of_fallacies" title="List of fallacies">Fallacies</a></li> <li><a href="/wiki/List_of_logic_symbols" title="List of logic symbols">Logic symbols</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="nowrap"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/18px-Socrates.png" decoding="async" width="18" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/27px-Socrates.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/36px-Socrates.png 2x" data-file-width="326" data-file-height="500" /></span></span> </span><a href="/wiki/Portal:Philosophy" title="Portal:Philosophy">Philosophy portal</a></li> <li><a href="/wiki/Category:Logic" title="Category:Logic">Category</a></li> <li><a href="/wiki/Wikipedia:WikiProject_Logic" title="Wikipedia:WikiProject Logic">WikiProject</a> (<a href="/wiki/Wikipedia_talk:WikiProject_Logic" title="Wikipedia talk:WikiProject Logic">talk</a>)</li> <li><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Special:Recentchangeslinked&target=Template:Logic&hidebots=0">changes</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Humanities" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Humanities" title="Template:Humanities"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Humanities" title="Template talk:Humanities"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Humanities" title="Special:EditPage/Template:Humanities"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Humanities" style="font-size:114%;margin:0 4em"><a href="/wiki/Humanities" title="Humanities">Humanities</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Disciplines</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0;height:2.5em;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Anthropology" title="Anthropology">Anthropology</a></li> <li><a href="/wiki/Archaeology" title="Archaeology">Archaeology</a></li> <li><a href="/wiki/Classics" title="Classics">Classical studies</a></li> <li><a href="/wiki/History" title="History">History</a></li> <li><a href="/wiki/The_arts#Literary_arts" title="The arts">Language arts</a> <ul><li><a href="/wiki/Literature" title="Literature">Literature</a></li> <li><a href="/wiki/Poetry" title="Poetry">Poetry</a></li> <li><a href="/wiki/Rhetoric" title="Rhetoric">Rhetoric</a></li></ul></li> <li><a href="/wiki/Law" title="Law">Law</a></li> <li><a href="/wiki/Performing_arts" title="Performing arts">Performing arts</a> <ul><li><a href="/wiki/Dance" title="Dance">Dance</a></li> <li><a href="/wiki/Musicology" title="Musicology">Music</a></li> <li><a href="/wiki/Theatre" title="Theatre">Theatre</a></li></ul></li> <li><a href="/wiki/Philosophy" title="Philosophy">Philosophy</a></li> <li><a href="/wiki/Religious_studies" title="Religious studies">Religious studies</a></li> <li><a href="/wiki/Visual_arts" title="Visual arts">Visual arts</a> <ul><li><a href="/wiki/Filmmaking" title="Filmmaking">Filmmaking</a></li> <li><a href="/wiki/Painting" title="Painting">Painting</a></li> <li><a href="/wiki/Sculpture" title="Sculpture">Sculpture</a></li></ul></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Interdisciplinary_fields" scope="row" class="navbox-group" style="width:1%">Interdisciplinary fields</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Digital_humanities" title="Digital humanities">Digital</a></li> <li><a href="/wiki/Environmental_humanities" title="Environmental humanities">Environmental</a></li> <li><a href="/wiki/Health_humanities" title="Health humanities">Health</a></li> <li><a href="/wiki/Medical_humanities" title="Medical humanities">Medical</a></li> <li><a href="/wiki/Public_humanities" title="Public humanities">Public</a></li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Themes</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Abductive reasoning</a></li> <li><a href="/wiki/Aesthetics" title="Aesthetics">Aesthetics</a></li> <li><a href="/wiki/Antipositivism" title="Antipositivism">Antipositivism</a></li> <li><a href="/wiki/The_arts" title="The arts">The arts</a></li> <li><a href="/wiki/Beauty" title="Beauty">Beauty</a></li> <li><i><a href="/wiki/Belles-lettres" title="Belles-lettres">Belles-lettres</a></i></li> <li><i><a href="/wiki/Bildung" title="Bildung">Bildung</a></i></li> <li><a href="/wiki/Creativity" title="Creativity">Creativity</a></li> <li><a href="/wiki/Critical_theory" title="Critical theory">Critical theory</a></li> <li><a href="/wiki/Criticism" title="Criticism">Criticism</a></li> <li><a href="/wiki/Cultural_literacy" title="Cultural literacy">Cultural literacy</a></li> <li><a href="/wiki/Culture" title="Culture">Culture</a> <ul><li><a href="/wiki/High_culture" title="High culture">High</a></li></ul></li> <li><a href="/wiki/General_knowledge" title="General knowledge">General knowledge</a></li> <li><a href="/wiki/Hermeneutics" title="Hermeneutics">Hermeneutics</a></li> <li> <a href="/wiki/Historicism" title="Historicism">Historicism</a></li> <li><a href="/wiki/Historism" title="Historism">Historism</a></li> <li><a href="/wiki/Human_condition" title="Human condition">Human condition</a></li> <li><i><a href="/wiki/Humanitas" title="Humanitas">Humanitas</a></i></li> <li><a href="/wiki/Liberal_arts_education" title="Liberal arts education">Liberal arts education</a> <ul><li><a href="/wiki/Trivium" title="Trivium">Trivium</a></li> <li><a href="/wiki/Quadrivium" title="Quadrivium">Quadrivium</a></li></ul></li> <li><a href="/wiki/Metaphysics" title="Metaphysics">Metaphysics</a> <ul><li><a href="/wiki/Ontology" title="Ontology">Ontology</a></li></ul></li> <li><a href="/wiki/Moral_character" title="Moral character">Moral character</a></li> <li><a href="/wiki/Self-realization" title="Self-realization">Self-realization</a></li> <li><a href="/wiki/Self-reflection" title="Self-reflection">Self-reflection</a></li> <li><a href="/wiki/Wisdom" title="Wisdom">Wisdom</a></li> <li><a href="/wiki/Work_of_art" title="Work of art">Work of art</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Journals</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0;font-style:italic;"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/American_Journal_of_Archaeology" title="American Journal of Archaeology">American Journal of Archaeology</a></li> <li><a href="/wiki/Daedalus_(journal)" title="Daedalus (journal)">Daedalus</a></li> <li><i><a href="/wiki/History_of_Humanities" title="History of Humanities">History of Humanities</a></i></li> <li><a href="/wiki/Humanitas_(journal)" title="Humanitas (journal)">Humanitas</a></li> <li><a href="/wiki/Humanities_and_Social_Sciences_Communications" title="Humanities and Social Sciences Communications">Humanities and Social Sciences Communications</a></li> <li><a href="/wiki/Journal_of_Controversial_Ideas" title="Journal of Controversial Ideas">Journal of Controversial Ideas</a></li> <li><a href="/wiki/Journal_of_the_Royal_Asiatic_Society" title="Journal of the Royal Asiatic Society">Journal of the Royal Asiatic Society</a></li> <li><a href="/wiki/Leonardo_(journal)" title="Leonardo (journal)">Leonardo</a></li> <li><a href="/wiki/Nova_Religio" title="Nova Religio">Nova Religio</a></li> <li><a href="/wiki/Revue_des_%C3%89tudes_Arm%C3%A9niennes" title="Revue des Études Arméniennes">Revue des Études Arméniennes</a></li> <li><a href="/wiki/Teaching_Philosophy" title="Teaching Philosophy">Teaching Philosophy</a></li> <li><i><a href="/wiki/List_of_humanities_journals" title="List of humanities journals">more...</a></i></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Academia</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Arts_and_Humanities_Research_Council" title="Arts and Humanities Research Council">Arts and Humanities Research Council</a></li> <li><a href="/wiki/Human_science" title="Human science">Human science</a> <ul><li><i><a href="/wiki/Geisteswissenschaft" title="Geisteswissenschaft">Geisteswissenschaft</a></i></li></ul></li> <li><a href="/wiki/Humanities,_arts,_and_social_sciences" title="Humanities, arts, and social sciences">Humanities, arts, and social sciences</a></li> <li><a href="/wiki/Master_of_Humanities" title="Master of Humanities">Master of Humanities</a></li> <li><a href="/wiki/Moscow_University_for_the_Humanities" title="Moscow University for the Humanities">Moscow University for the Humanities</a></li> <li><a href="/wiki/National_Endowment_for_the_Humanities" title="National Endowment for the Humanities">National Endowment for the Humanities</a></li> <li><a href="/wiki/National_Humanities_Medal" title="National Humanities Medal">National Humanities Medal</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Antihumanism" title="Antihumanism">Antihumanism</a> <ul><li><a href="/wiki/Philistinism" title="Philistinism">Philistinism</a></li></ul></li> <li><a href="/wiki/Popular_culture#Criticism" title="Popular culture">Criticism of mass culture</a></li> <li><a href="/wiki/Educational_essentialism" title="Educational essentialism">Educational essentialism</a></li> <li><a href="/wiki/Humanities_in_the_United_States" title="Humanities in the United States">Humanities in the United States</a></li> <li><a href="/wiki/List_of_people_considered_a_founder_in_a_Humanities_field" class="mw-redirect" title="List of people considered a founder in a Humanities field">List of people considered a founder in a Humanities field</a></li> <li><a href="/wiki/Outline_of_the_humanities" title="Outline of the humanities">Outline of the humanities</a></li> <li><a href="/wiki/Renaissance_humanism" title="Renaissance humanism">Renaissance humanism</a></li> <li><i><a href="/wiki/Latin_school#Studia_Humanitatis" title="Latin school">Studia Humanitatis</a></i></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235"></div><div role="navigation" class="navbox" aria-labelledby="Philosophical_logic" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Philosophical_logic" title="Template:Philosophical logic"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Philosophical_logic" title="Template talk:Philosophical logic"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Philosophical_logic" title="Special:EditPage/Template:Philosophical logic"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Philosophical_logic" style="font-size:114%;margin:0 4em"><a href="/wiki/Philosophical_logic" title="Philosophical logic">Philosophical logic</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Critical_thinking" title="Critical thinking">Critical thinking</a> and<br /><a href="/wiki/Informal_logic" title="Informal logic">informal logic</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Philosophical_analysis" title="Philosophical analysis">Analysis</a></li> <li><a href="/wiki/Ambiguity" title="Ambiguity">Ambiguity</a></li> <li><a href="/wiki/Argument" title="Argument">Argument</a></li> <li><a href="/wiki/Belief" title="Belief">Belief</a></li> <li><a href="/wiki/Bias" title="Bias">Bias</a></li> <li><a href="/wiki/Credibility" title="Credibility">Credibility</a></li> <li><a href="/wiki/Dialectic" title="Dialectic">Dialectic</a> <ul><li><a href="/wiki/Antithesis" title="Antithesis">Antithesis</a>, <a href="/wiki/Socratic_method" title="Socratic method">Socratic method</a>, <a href="/wiki/Unity_of_opposites" title="Unity of opposites">Unity of opposites</a></li></ul></li> <li><a href="/wiki/Evidence" title="Evidence">Evidence</a></li> <li><a href="/wiki/Explanation" title="Explanation">Explanation</a></li> <li><a href="/wiki/Explanatory_power" title="Explanatory power">Explanatory power</a></li> <li><a href="/wiki/Fact" title="Fact">Fact</a></li> <li><a href="/wiki/Fallacy" title="Fallacy">Fallacy</a> <ul><li><a href="/wiki/List_of_fallacies" title="List of fallacies">List of fallacies</a></li></ul></li> <li><a href="/wiki/Hypothesis" title="Hypothesis">Hypothesis</a></li> <li><a href="/wiki/Inquiry" title="Inquiry">Inquiry</a></li> <li><a href="/wiki/Opinion" title="Opinion">Opinion</a></li> <li><a href="/wiki/Occam%27s_razor" title="Occam's razor">Parsimony (Occam's razor)</a></li> <li><a href="/wiki/Premise" title="Premise">Premise</a></li> <li><a href="/wiki/Propaganda" title="Propaganda">Propaganda</a></li> <li><a href="/wiki/Prudence" title="Prudence">Prudence</a></li> <li><a href="/wiki/Reason" title="Reason">Reasoning</a></li> <li><a href="/wiki/Relevance" title="Relevance">Relevance</a></li> <li><a href="/wiki/Rhetoric" title="Rhetoric">Rhetoric</a></li> <li><a href="/wiki/Rigour" title="Rigour">Rigor</a></li> <li><a href="/wiki/Theory" title="Theory">Theory</a></li> <li><a href="/wiki/Vagueness" title="Vagueness">Vagueness</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Deductive_reasoning" title="Deductive reasoning">Theories of deduction</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Constructivism_(philosophy_of_mathematics)" title="Constructivism (philosophy of mathematics)">Constructivism</a></li> <li><a href="/wiki/Dialetheism" title="Dialetheism">Dialetheism</a></li> <li><a href="/wiki/Fictionalism" title="Fictionalism">Fictionalism</a></li> <li><a href="/wiki/Finitism" title="Finitism">Finitism</a></li> <li><a href="/wiki/Formalism_(mathematics)" class="mw-redirect" title="Formalism (mathematics)">Formalism</a></li> <li><a href="/wiki/Intuitionism" title="Intuitionism">Intuitionism</a></li> <li><a href="/wiki/Logical_atomism" title="Logical atomism">Logical atomism</a></li> <li><a href="/wiki/Logicism" title="Logicism">Logicism</a></li> <li><a href="/wiki/Nominalism" title="Nominalism">Nominalism</a></li> <li><a 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