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non classiques</span> </div> </a> <ul id="toc-Logiques_non_classiques-sublist" class="vector-toc-list"> <li id="toc-Logique_intuitionniste" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Logique_intuitionniste"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.1</span> <span>Logique intuitionniste</span> </div> </a> <ul id="toc-Logique_intuitionniste-sublist" class="vector-toc-list"> <li id="toc-Un_exemple" class="vector-toc-list-item vector-toc-level-4"> <a class="vector-toc-link" href="#Un_exemple"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.1.1</span> <span>Un exemple</span> </div> </a> <ul id="toc-Un_exemple-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Logiques_modales" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Logiques_modales"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.2</span> <span>Logiques modales</span> </div> </a> <ul id="toc-Logiques_modales-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Systèmes_complets_de_connecteurs" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Systèmes_complets_de_connecteurs"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Systèmes complets de connecteurs</span> </div> </a> <ul id="toc-Systèmes_complets_de_connecteurs-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notes_et_références" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notes_et_références"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Notes et références</span> </div> </a> <ul id="toc-Notes_et_références-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="Sommaire" 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="Basculer la table des matières" > <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">Basculer la table des matières</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">Connecteur logique</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="Aller à un article dans une autre langue. Disponible en 39 langues." > <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-39" 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">39 langues</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/%D8%B1%D8%A7%D8%A8%D8%B7%D8%A9_%D9%85%D9%86%D8%B7%D9%82%D9%8A%D8%A9" title="رابطة منطقية – arabe" lang="ar" hreflang="ar" data-title="رابطة منطقية" data-language-autonym="العربية" data-language-local-name="arabe" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/M%C9%99ntiqi_%C9%99m%C9%99liyyat" title="Məntiqi əməliyyat – azerbaïdjanais" lang="az" hreflang="az" data-title="Məntiqi əməliyyat" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaïdjanais" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F" title="Логическа операция – bulgare" lang="bg" hreflang="bg" data-title="Логическа операция" data-language-autonym="Български" data-language-local-name="bulgare" 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/Connectiva_l%C3%B2gica" title="Connectiva lògica – catalan" lang="ca" hreflang="ca" data-title="Connectiva lògica" data-language-autonym="Català" data-language-local-name="catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Logisk_operator" title="Logisk operator – danois" lang="da" hreflang="da" data-title="Logisk operator" data-language-autonym="Dansk" data-language-local-name="danois" 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/Logische_Verkn%C3%BCpfung" title="Logische Verknüpfung – allemand" lang="de" hreflang="de" data-title="Logische Verknüpfung" data-language-autonym="Deutsch" data-language-local-name="allemand" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9B%CE%BF%CE%B3%CE%B9%CE%BA%CE%AD%CF%82_%CF%83%CF%85%CE%BD%CE%B1%CF%81%CF%84%CE%AE%CF%83%CE%B5%CE%B9%CF%82" title="Λογικές συναρτήσεις – grec" lang="el" hreflang="el" data-title="Λογικές συναρτήσεις" data-language-autonym="Ελληνικά" data-language-local-name="grec" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/Conet%C3%AEv_l%C3%B2gic" title="Conetîv lògic – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Conetîv lògic" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Logical_connective" title="Logical connective – anglais" lang="en" hreflang="en" data-title="Logical connective" data-language-autonym="English" data-language-local-name="anglais" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Conectiva_l%C3%B3gica" title="Conectiva lógica – espagnol" lang="es" hreflang="es" data-title="Conectiva lógica" data-language-autonym="Español" data-language-local-name="espagnol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Konnektor_(keeleteadus)" title="Konnektor (keeleteadus) – estonien" lang="et" hreflang="et" data-title="Konnektor (keeleteadus)" data-language-autonym="Eesti" data-language-local-name="estonien" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Lokailu_logiko" title="Lokailu logiko – basque" lang="eu" hreflang="eu" data-title="Lokailu logiko" data-language-autonym="Euskara" data-language-local-name="basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D8%A7%D8%A8%D8%B7_%D9%85%D9%86%D8%B7%D9%82%DB%8C" title="رابط منطقی – persan" lang="fa" hreflang="fa" data-title="رابط منطقی" data-language-autonym="فارسی" data-language-local-name="persan" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%A9%D7%A8_%D7%9C%D7%95%D7%92%D7%99" title="קשר לוגי – hébreu" lang="he" hreflang="he" data-title="קשר לוגי" data-language-autonym="עברית" data-language-local-name="hébreu" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Logikai_m%C5%B1velet" title="Logikai művelet – hongrois" lang="hu" hreflang="hu" data-title="Logikai művelet" data-language-autonym="Magyar" data-language-local-name="hongrois" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8F%D6%80%D5%A1%D5%B4%D5%A1%D5%A2%D5%A1%D5%B6%D5%A1%D5%AF%D5%A1%D5%B6_%D5%A3%D5%B8%D6%80%D5%AE%D5%B8%D5%B2%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Տրամաբանական գործողություն – arménien" lang="hy" hreflang="hy" data-title="Տրամաբանական գործողություն" data-language-autonym="Հայերեն" data-language-local-name="arménien" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Operator_logika" title="Operator logika – indonésien" lang="id" hreflang="id" data-title="Operator logika" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésien" 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/R%C3%B6ka%C3%B0ger%C3%B0" title="Rökaðgerð – islandais" lang="is" hreflang="is" data-title="Rökaðgerð" data-language-autonym="Íslenska" data-language-local-name="islandais" 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/Connettivo_logico" title="Connettivo logico – italien" lang="it" hreflang="it" data-title="Connettivo logico" data-language-autonym="Italiano" data-language-local-name="italien" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%AB%96%E7%90%86%E6%BC%94%E7%AE%97" title="論理演算 – japonais" lang="ja" hreflang="ja" data-title="論理演算" data-language-autonym="日本語" data-language-local-name="japonais" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D0%BF%D0%BE%D0%B7%D0%B8%D1%86%D0%B8%D1%8F%D0%BB%D1%8B%D2%9B_%D3%A9%D0%B7%D0%B0%D1%80%D0%B0_%D2%9B%D0%B0%D1%82%D1%8B%D0%BD%D0%B0%D1%81" title="Пропозициялық өзара қатынас – kazakh" lang="kk" hreflang="kk" data-title="Пропозициялық өзара қатынас" data-language-autonym="Қазақша" data-language-local-name="kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%85%BC%EB%A6%AC_%EC%97%B0%EC%82%B0" title="논리 연산 – coréen" lang="ko" hreflang="ko" data-title="논리 연산" data-language-autonym="한국어" data-language-local-name="coréen" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B8%D1%87%D0%BA%D0%B0_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Логичка операција – macédonien" lang="mk" hreflang="mk" data-title="Логичка операција" data-language-autonym="Македонски" data-language-local-name="macédonien" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pengoperasi_logik" title="Pengoperasi logik – malais" lang="ms" hreflang="ms" data-title="Pengoperasi logik" data-language-autonym="Bahasa Melayu" data-language-local-name="malais" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Logisk_konstant" title="Logisk konstant – norvégien nynorsk" lang="nn" hreflang="nn" data-title="Logisk konstant" data-language-autonym="Norsk nynorsk" data-language-local-name="norvégien nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Funktor_zdaniotw%C3%B3rczy" title="Funktor zdaniotwórczy – polonais" lang="pl" hreflang="pl" data-title="Funktor zdaniotwórczy" data-language-autonym="Polski" data-language-local-name="polonais" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Conectivo_l%C3%B3gico" title="Conectivo lógico – portugais" lang="pt" hreflang="pt" data-title="Conectivo lógico" data-language-autonym="Português" data-language-local-name="portugais" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Conector_logic" title="Conector logic – roumain" lang="ro" hreflang="ro" data-title="Conector logic" data-language-autonym="Română" data-language-local-name="roumain" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F" title="Логическая операция – russe" lang="ru" hreflang="ru" data-title="Логическая операция" data-language-autonym="Русский" data-language-local-name="russe" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/V%C3%BDrokov%C3%A1_spojka" title="Výroková spojka – slovaque" lang="sk" hreflang="sk" data-title="Výroková spojka" data-language-autonym="Slovenčina" data-language-local-name="slovaque" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Logisk_operator" title="Logisk operator – suédois" lang="sv" hreflang="sv" data-title="Logisk operator" data-language-autonym="Svenska" data-language-local-name="suédois" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%8F%E0%AE%B0%E0%AE%A3_%E0%AE%87%E0%AE%A3%E0%AF%88%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AE%BF" title="ஏரண இணைப்பி – tamoul" lang="ta" hreflang="ta" data-title="ஏரண இணைப்பி" data-language-autonym="தமிழ்" data-language-local-name="tamoul" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%BC%D0%B0%D0%BB%D2%B3%D0%BE%D0%B8_%D0%BC%D0%B0%D0%BD%D1%82%D0%B8%D2%9B%D3%A3" title="Амалҳои мантиқӣ – tadjik" lang="tg" hreflang="tg" data-title="Амалҳои мантиқӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="tadjik" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B8%94%E0%B8%B3%E0%B9%80%E0%B8%99%E0%B8%B4%E0%B8%99%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%95%E0%B8%A3%E0%B8%A3%E0%B8%81%E0%B8%B0" title="ตัวดำเนินการตรรกะ – thaï" lang="th" hreflang="th" data-title="ตัวดำเนินการตรรกะ" data-language-autonym="ไทย" data-language-local-name="thaï" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Mant%C4%B1k_ba%C4%9Flac%C4%B1" title="Mantık bağlacı – turc" lang="tr" hreflang="tr" data-title="Mantık bağlacı" data-language-autonym="Türkçe" data-language-local-name="turc" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D1%96%D1%87%D0%BD%D0%B8%D0%B9_%D1%81%D0%BF%D0%BE%D0%BB%D1%83%D1%87%D0%BD%D0%B8%D0%BA" title="Логічний сполучник – ukrainien" lang="uk" hreflang="uk" data-title="Логічний сполучник" data-language-autonym="Українська" data-language-local-name="ukrainien" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D9%86%D8%B7%D9%82%DB%8C_%D8%B9%D8%A7%D9%85%D9%84" title="منطقی عامل – ourdou" lang="ur" hreflang="ur" data-title="منطقی عامل" data-language-autonym="اردو" data-language-local-name="ourdou" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" title="逻辑运算符 – chinois" lang="zh" hreflang="zh" data-title="逻辑运算符" data-language-autonym="中文" data-language-local-name="chinois" 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href="/wiki/Aide:Homonymie" title="Aide:Homonymie"><img alt="Page d’aide sur l’homonymie" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/20px-Logo_disambig.svg.png" decoding="async" width="20" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/30px-Logo_disambig.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Logo_disambig.svg/40px-Logo_disambig.svg.png 2x" data-file-width="512" data-file-height="375" /></a></span></div><div class="bandeau-cell" style="display:table-cell;padding-right:0.5em"> <p>Pour l’article homonyme, voir <a href="/wiki/Connecteur_logique_(linguistique)" title="Connecteur logique (linguistique)">Connecteur logique (linguistique)</a>. </p> </div></div> <p>En <a href="/wiki/Logique" title="Logique">logique</a>, un <b>connecteur logique</b> est un <a href="/wiki/Op%C3%A9rateur_(symbole)" title="Opérateur (symbole)">opérateur</a> <a href="/wiki/Bool%C3%A9en" title="Booléen">booléen</a> utilisé dans le calcul des propositions. </p><p>Comme dans toute approche logique, il faut distinguer un aspect <a href="/wiki/Logique_math%C3%A9matique#Syntaxe_et_sémantique" title="Logique mathématique">syntaxique</a> et un aspect <a href="/wiki/Logique_math%C3%A9matique#Syntaxe_et_sémantique" title="Logique mathématique">sémantique</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Syntaxe">Syntaxe</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Connecteur_logique&veaction=edit&section=1" title="Modifier la section : Syntaxe" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Connecteur_logique&action=edit&section=1" title="Modifier le code source de la section : Syntaxe"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>D'un point de vue syntaxique, les connecteurs sont des <a href="/wiki/Op%C3%A9rateur_(symbole)" title="Opérateur (symbole)">opérateurs</a> dans un <a href="/wiki/Langage_formel" title="Langage formel">langage formel</a> pour lesquels un certain nombre de <a href="/wiki/D%C3%A9duction_logique" title="Déduction logique">règles</a> définissent leur usage<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite_crochet">[</span>1<span class="cite_crochet">]</span></a></sup>, au besoin complétées par une sémantique. </p> <div class="mw-heading mw-heading2"><h2 id="Sémantique"><span id="S.C3.A9mantique"></span>Sémantique</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Connecteur_logique&veaction=edit&section=2" title="Modifier la section : Sémantique" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a 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href="/wiki/Bool%C3%A9en" title="Booléen">booléens</a> ou dans une extension <a href="/wiki/Logique_polyvalente" title="Logique polyvalente">multivalente</a><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite_crochet">[</span>2<span class="cite_crochet">]</span></a></sup> de ceux-ci. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichier:Logical_connectives_table.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Logical_connectives_table.svg/220px-Logical_connectives_table.svg.png" decoding="async" width="220" height="286" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Logical_connectives_table.svg/330px-Logical_connectives_table.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Logical_connectives_table.svg/440px-Logical_connectives_table.svg.png 2x" data-file-width="547" data-file-height="710" /></a><figcaption>Table des connecteurs logiques. <i>(organisés par valeur de vérité)</i></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fichier:Logical_connectives_Hasse_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/220px-Logical_connectives_Hasse_diagram.svg.png" decoding="async" width="220" height="311" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/330px-Logical_connectives_Hasse_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/440px-Logical_connectives_Hasse_diagram.svg.png 2x" data-file-width="744" data-file-height="1052" /></a><figcaption>Connecteurs logiques organisés en un <a href="/wiki/Diagramme_de_Hasse" title="Diagramme de Hasse">diagramme de Hasse</a>.</figcaption></figure> <p>Dans le cas de la logique bivalente <a href="/wiki/Logique_classique" title="Logique classique">classique</a> le tableau suivant recense les seize <a href="/wiki/Fonction_bool%C3%A9enne" title="Fonction booléenne">fonctions booléennes</a> associées aux entrées P et Q, ces entrées sont les variables ou prémisses des formules. </p> <table class="wikitable" style="text-align:center"> <tbody><tr> <th scope="col">Fonction booléenne </th> <th scope="col">Notations </th> <th scope="col">Formules équivalentes </th> <th scope="col"><a href="/wiki/Table_de_v%C3%A9rit%C3%A9" title="Table de vérité">Table de vérité</a> </th> <th scope="col"><a href="/wiki/Diagramme_de_Venn" title="Diagramme de Venn">Diagramme de Venn</a> </th></tr> <tr> <th style="text-align: left"><a href="/wiki/Calcul_des_propositions" title="Calcul des propositions">Proposition</a> P </th> <td><i>P</i> </td> <td> </td> <td> <table class="wikitable" style="background:none; text-align: center; border: 0px;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 0px;">  </td> <td colspan="2" style="border: 0px;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle; border:0px;"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn0101.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Venn0101.svg/100px-Venn0101.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Venn0101.svg/150px-Venn0101.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/10/Venn0101.svg/200px-Venn0101.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr> <tr> <th style="text-align: left"><a href="/wiki/Calcul_des_propositions" title="Calcul des propositions">Proposition</a> <i>Q</i> </th> <td><i>Q</i> </td> <td> </td> <td> <table style="background:none; text-align: center; border: 0px;" class="wikitable"> <tbody><tr> <td style="border: 0px;" rowspan="2" colspan="2">  </td> <td style="border: 0px;" colspan="2"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td style="vertical-align: middle; border:0px;" rowspan="2"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn0011.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/Venn0011.svg/100px-Venn0011.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/Venn0011.svg/150px-Venn0011.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/76/Venn0011.svg/200px-Venn0011.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr> <tr> <th style="text-align: left"><a href="/wiki/N%C3%A9gation_logique" title="Négation logique">Négation</a> de P </th> <td>¬<i>P</i><br />~<i>P</i> </td> <td> </td> <td> <table style="background:none; text-align: center; border: 0px;" class="wikitable"> <tbody><tr> <td style="border: 0px;" rowspan="2" colspan="2">  </td> <td style="border: 0px;" colspan="2"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td style="vertical-align: middle; border:0px;" rowspan="2"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn1010.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Venn1010.svg/100px-Venn1010.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Venn1010.svg/150px-Venn1010.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Venn1010.svg/200px-Venn1010.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr> <tr> <th style="text-align: left"><a href="/wiki/N%C3%A9gation_logique" title="Négation logique">Négation</a> de <i>Q</i> </th> <td>¬<i>Q</i><br />~<i>Q</i> </td> <td> </td> <td> <table style="background:none; text-align: center; border: 0px;" class="wikitable"> <tbody><tr> <td style="border: 0px;" rowspan="2" colspan="2">  </td> <td style="border: 0px;" colspan="2"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td style="vertical-align: middle; border:0px;" rowspan="2"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn1100.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Venn1100.svg/100px-Venn1100.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Venn1100.svg/150px-Venn1100.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/Venn1100.svg/200px-Venn1100.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr> <tr> <th> </th> <th> </th> <th> </th> <th> </th> <th> </th></tr> <tr> <th style="text-align: left"><a href="/wiki/Disjonction_logique" title="Disjonction logique">Disjonction</a><br />(OU) </th> <td><i>P</i> <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 \lor }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lor }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab47f6b1f589aedcf14638df1d63049d233d851a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \lor }"></span> <i>Q</i><br /><i>P</i> <sub>∨</sub> <i>Q</i><br /><i>P</i> OR <i>Q</i> </td> <td><i>P</i> <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 \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">←</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c0fb4bce772117bbaf55b7ca1539ceff9ae218c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftarrow }"></span> ¬<i>Q</i> <br /> ¬<i>P</i> → <i>Q</i> <br /> ¬<i>P</i> ↑ ¬<i>Q</i> </td> <td> <table style="background:none; text-align: center; border: 0px;" class="wikitable"> <tbody><tr> <td style="border: 0px;" rowspan="2" colspan="2">  </td> <td style="border: 0px;" colspan="2"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td style="vertical-align: middle; border:0px;" rowspan="2"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn0111.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/100px-Venn0111.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/150px-Venn0111.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/200px-Venn0111.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr> <tr> <th style="text-align: left"><a href="/wiki/Conjonction_logique" title="Conjonction logique">Conjonction</a> <br />(ET) </th> <td><i>P</i> <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 \wedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1caa4004cb216ef2930bb12fe805a76870caed94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \wedge }"></span> <i>Q</i><br /><i>P</i> & <i>Q</i><br /><i>P</i> <b>·</b> <i>Q</i><br /><i>P</i> AND <i>Q</i> </td> <td><i>P</i> <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 \not \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↛</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb95f3f5a9898c871045935a253d1d23e0e2644b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \rightarrow }"></span>¬<i>Q</i> <br /> ¬<i>P</i> <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 \not \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↚</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4acf12661d69611db01ff7f036bf8c5b5dfec902" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftarrow }"></span> <i>Q</i> <br /> ¬<i>P</i> <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 \downarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↓</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \downarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4618f22b0f780805eb94bb407578d9bc9487947a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.162ex; height:2.509ex;" alt="{\displaystyle \downarrow }"></span> ¬<i>Q</i> </td> <td> <table style="background:none; text-align: center; border: 0px;" class="wikitable"> <tbody><tr> <td style="border: 0px;" rowspan="2" colspan="2">  </td> <td style="border: 0px;" colspan="2"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td style="vertical-align: middle; border:0px;" rowspan="2"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn0001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/100px-Venn0001.svg.png" decoding="async" width="100" height="73" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/150px-Venn0001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/200px-Venn0001.svg.png 2x" data-file-width="410" data-file-height="299" /></a></span> </td></tr> <tr> <th style="text-align: left"><a href="/wiki/Fonction_NON-OU" title="Fonction NON-OU">Disjonction réciproque</a><br />(NON-OU) </th> <td><i>P</i> ↓ <i>Q</i><br /><i>P</i> NOR <i>Q</i> </td> <td><i>P</i> <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 \not \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↚</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4acf12661d69611db01ff7f036bf8c5b5dfec902" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftarrow }"></span> ¬<i>Q</i> <br /> ¬<i>P</i> <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 \not \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↛</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb95f3f5a9898c871045935a253d1d23e0e2644b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \rightarrow }"></span> <i>Q</i> <br /> ¬<i>P</i> <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 \wedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1caa4004cb216ef2930bb12fe805a76870caed94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \wedge }"></span> ¬<i>Q</i> </td> <td> <table style="background:none; text-align: center; border: 0px;" class="wikitable"> <tbody><tr> <td style="border: 0px;" rowspan="2" colspan="2">  </td> <td style="border: 0px;" colspan="2"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td style="vertical-align: middle; border:0px;" rowspan="2"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn1000.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Venn1000.svg/100px-Venn1000.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Venn1000.svg/150px-Venn1000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Venn1000.svg/200px-Venn1000.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr> <tr> <th style="text-align: left"><a href="/wiki/Fonction_NON-ET" title="Fonction NON-ET">NON-ET</a> </th> <td><i>P</i> ↑ <i>Q</i><br /><i>P</i> | <i>Q</i> <br /><i>P</i> NAND <i>Q</i> </td> <td><i>P</i> → ¬<i>Q</i> <br /> ¬<i>P</i> ← <i>Q</i><br />¬<i>P</i> <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 \lor }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lor }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab47f6b1f589aedcf14638df1d63049d233d851a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \lor }"></span> ¬<i>Q</i> </td> <td> <table style="background:none; text-align: center; border: 0px;" class="wikitable"> <tbody><tr> <td style="border: 0px;" rowspan="2" colspan="2">  </td> <td style="border: 0px;" colspan="2"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td style="vertical-align: middle; border:0px;" rowspan="2"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn1110.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Venn1110.svg/100px-Venn1110.svg.png" decoding="async" width="100" height="73" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Venn1110.svg/150px-Venn1110.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Venn1110.svg/200px-Venn1110.svg.png 2x" data-file-width="410" data-file-height="299" /></a></span> </td></tr> <tr> <th> </th> <th> </th> <th> </th> <th> </th> <th> </th></tr> <tr> <th style="text-align: left"><a href="/wiki/Contradiction" title="Contradiction">Contradiction</a> </th> <td><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 \bot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">⊥</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f282c7bc331cc3bfcf1c57f1452cc23c022f58de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \bot }"></span>FALSE </td> <td><i>P</i> <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 \wedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1caa4004cb216ef2930bb12fe805a76870caed94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \wedge }"></span> ¬<i>P</i> </td> <td> <table style="background:none; text-align: center; border: 0px;" class="wikitable"> <tbody><tr> <td style="border: 0px;" rowspan="2" colspan="2">  </td> <td style="border: 0px;" colspan="2"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td style="vertical-align: middle; border:0px;" rowspan="2"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn0000.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Venn0000.svg/100px-Venn0000.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Venn0000.svg/150px-Venn0000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Venn0000.svg/200px-Venn0000.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr> <tr> <th style="text-align: left"><a href="/wiki/Tautologie_(logique)" title="Tautologie (logique)">Tautologie</a> </th> <td><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 \top }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">⊤</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \top }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf12e436fef2365e76fcb1034a51179d8328bb33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \top }"></span>TRUE </td> <td><i>P</i> <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 \vee }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \vee }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b76220c6805c9b465d6efbc7686c624f49f3023" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \vee }"></span> ¬<i>P</i> </td> <td> <table style="background:none; text-align: center; border: 0px;" class="wikitable"> <tbody><tr> <td style="border: 0px;" rowspan="2" colspan="2">  </td> <td style="border: 0px;" colspan="2"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td style="vertical-align: middle; border:0px;" rowspan="2"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn1111.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Venn1111.svg/100px-Venn1111.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Venn1111.svg/150px-Venn1111.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Venn1111.svg/200px-Venn1111.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr> <tr> <th> </th> <th> </th> <th> </th> <th> </th> <th> </th></tr> <tr> <th style="text-align: left"><a href="/wiki/Implication_(logique)" title="Implication (logique)">Implication</a> </th> <td><i>P</i> → <i>Q</i> <br /> <i>P</i> <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 \supset }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊃</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \supset }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27bfe0828a2ed4c9c6b70987a85c02a1f005843c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:1.843ex;" alt="{\displaystyle \supset }"></span> <i>Q</i> </td> <td><i>P</i> ↑ ¬<i>Q</i> <br /> ¬<i>P</i> <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 \lor }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lor }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab47f6b1f589aedcf14638df1d63049d233d851a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \lor }"></span> <i>Q</i> <br /> ¬<i>P</i> ← ¬<i>Q</i> </td> <td> <table style="background:none; text-align: center; border: 0px;" class="wikitable"> <tbody><tr> <td style="border: 0px;" rowspan="2" colspan="2">  </td> <td style="border: 0px;" colspan="2"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td style="vertical-align: middle; border:0px;" rowspan="2"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn1011.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Venn1011.svg/100px-Venn1011.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Venn1011.svg/150px-Venn1011.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Venn1011.svg/200px-Venn1011.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr> <tr> <th style="text-align: left"><a href="/wiki/Implication_r%C3%A9ciproque" title="Implication réciproque">Implication réciproque</a> </th> <td><i>P</i> <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 \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">←</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c0fb4bce772117bbaf55b7ca1539ceff9ae218c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftarrow }"></span> <i>Q</i> <br /> <i>P</i> <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 \subset }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊂</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \subset }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f51f0eeff0c2a9dcb9c856f87ca0359e701ef01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:1.843ex;" alt="{\displaystyle \subset }"></span> <i>Q</i> </td> <td><i>P</i> <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 \lor }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lor }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab47f6b1f589aedcf14638df1d63049d233d851a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \lor }"></span> ¬<i>Q</i> <br /> ¬<i>P</i> ↑ <i>Q</i> <br /> ¬<i>P</i> → ¬<i>Q</i> </td> <td> <table style="background:none; text-align: center; border: 0px;" class="wikitable"> <tbody><tr> <td style="border: 0px;" rowspan="2" colspan="2">  </td> <td style="border: 0px;" colspan="2"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td style="vertical-align: middle; border:0px;" rowspan="2"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn1101.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Venn1101.svg/100px-Venn1101.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Venn1101.svg/150px-Venn1101.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/Venn1101.svg/200px-Venn1101.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr> <tr> <th style="text-align: left"><a href="/wiki/Non-implication" title="Non-implication">Non-implication</a> </th> <td><i>P</i> <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 \not \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↛</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb95f3f5a9898c871045935a253d1d23e0e2644b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \rightarrow }"></span> <i>Q</i> <br /> <i>P</i> <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 \not \supset }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊅</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \supset }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0066ef658b08a8a21cf267a4e5bec61bc03fcb73" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.809ex; height:2.676ex;" alt="{\displaystyle \not \supset }"></span> <i>Q</i> </td> <td><i>P</i> <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 \wedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1caa4004cb216ef2930bb12fe805a76870caed94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \wedge }"></span> ¬<i>Q</i> <br /> ¬<i>P</i> ↓ <i>Q</i> <br /> ¬<i>P</i> <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 \not \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↚</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4acf12661d69611db01ff7f036bf8c5b5dfec902" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftarrow }"></span> ¬<i>Q</i> </td> <td> <table style="background:none; text-align: center; border: 0px;" class="wikitable"> <tbody><tr> <td style="border: 0px;" rowspan="2" colspan="2">  </td> <td style="border: 0px;" colspan="2"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td style="vertical-align: middle; border:0px;" rowspan="2"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn0100.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Venn0100.svg/100px-Venn0100.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Venn0100.svg/150px-Venn0100.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Venn0100.svg/200px-Venn0100.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr> <tr> <th style="text-align: left"><a href="/wiki/Non-implication_r%C3%A9ciproque" title="Non-implication réciproque">Non-implication réciproque</a> </th> <td><i>P</i> <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 \not \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↚</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4acf12661d69611db01ff7f036bf8c5b5dfec902" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftarrow }"></span> <i>Q</i> <br /> <i>P</i> <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 \not \subset }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊄</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \subset }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b8e16e392d3856efb6355f906bf3d7b35f7f2ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.809ex; height:2.676ex;" alt="{\displaystyle \not \subset }"></span> <i>Q</i> </td> <td><i>P</i> ↓ ¬<i>Q</i> <br /> ¬<i>P</i> <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 \wedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1caa4004cb216ef2930bb12fe805a76870caed94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \wedge }"></span> <i>Q</i> <br /> ¬<i>P</i> <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 \not \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↛</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb95f3f5a9898c871045935a253d1d23e0e2644b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \rightarrow }"></span> ¬<i>Q</i> </td> <td> <table style="background:none; text-align: center; border: 0px;" class="wikitable"> <tbody><tr> <td style="border: 0px;" rowspan="2" colspan="2">  </td> <td style="border: 0px;" colspan="2"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td style="vertical-align: middle; border:0px;" rowspan="2"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn0010.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Venn0010.svg/100px-Venn0010.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Venn0010.svg/150px-Venn0010.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Venn0010.svg/200px-Venn0010.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr> <tr> <th> </th> <th> </th> <th> </th> <th> </th> <th> </th></tr> <tr> <th style="text-align: left"><a href="/wiki/%C3%89quivalence_logique" title="Équivalence logique">Équivalence</a> </th> <td><i>P</i> <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 \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/046b918c43e05caf6624fe9b676c69ec9cd6b892" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftrightarrow }"></span> <i>Q</i> <br /> <i>P</i> ≡ <i>Q</i><br /> <i>P</i> <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 \odot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊙</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \odot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e89e009eb8a8839c82aa5c76c15e9f2d67006276" 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 \odot }"></span> <i>Q</i> <br /> <i>P</i> XNOR <i>Q</i><br /> <i>P</i> IFF <i>Q</i> </td> <td><i>P</i> <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 \not \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↮</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/363ed81fd02da85c658dde9f17737c13b7263e49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftrightarrow }"></span> ¬<i>Q</i> <br /> ¬<i>P</i> <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 \not \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↮</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/363ed81fd02da85c658dde9f17737c13b7263e49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftrightarrow }"></span> <i>Q</i> <br /> ¬<i>P</i> <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 \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/046b918c43e05caf6624fe9b676c69ec9cd6b892" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftrightarrow }"></span> ¬<i>Q</i> </td> <td> <table style="background:none; text-align: center; border: 0px;" class="wikitable"> <tbody><tr> <td style="border: 0px;" rowspan="2" colspan="2">  </td> <td style="border: 0px;" colspan="2"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td style="vertical-align: middle; border:0px;" rowspan="2"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn1001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Venn1001.svg/100px-Venn1001.svg.png" decoding="async" width="100" height="73" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Venn1001.svg/150px-Venn1001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Venn1001.svg/200px-Venn1001.svg.png 2x" data-file-width="410" data-file-height="299" /></a></span> </td></tr> <tr> <th style="text-align: left"><a href="/wiki/Fonction_OU_exclusif" title="Fonction OU exclusif">Disjonction exclusive</a><br />(OU exclusif) </th> <td><i>P</i> <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 \not \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↮</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/363ed81fd02da85c658dde9f17737c13b7263e49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftrightarrow }"></span> <i>Q</i> <br /> <i>P</i> <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 \not \equiv }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≢</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \equiv }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d130bfc3eff6deb5c732a636f866cd9e373c197" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.809ex; height:2.676ex;" alt="{\displaystyle \not \equiv }"></span> <i>Q</i> <br /> <i>P</i> <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 \oplus }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊕</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oplus }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b16e2bdaefee9eed86d866e6eba3ac47c710f60" 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 \oplus }"></span> <i>Q</i><br /><i>P</i> XOR <i>Q</i> </td> <td><i>P</i> <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 \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/046b918c43e05caf6624fe9b676c69ec9cd6b892" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftrightarrow }"></span> ¬<i>Q</i> <br /> ¬<i>P</i> <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 \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/046b918c43e05caf6624fe9b676c69ec9cd6b892" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftrightarrow }"></span> <i>Q</i> <br /> ¬<i>P</i> <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 \not \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↮</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/363ed81fd02da85c658dde9f17737c13b7263e49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftrightarrow }"></span> ¬<i>Q</i> </td> <td> <table class="wikitable" style="background:none; text-align: center; border: 0px;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 0px;">  </td> <td colspan="2" style="border: 0px;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt; border: 0px;">0 </td> <td style="padding: 4pt; border: 0px;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle; border:0px;"><b>P</b> </td> <td style="border: 0px;">0   </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td></tr> <tr> <td style="padding: 4pt; border:0px;">1   </td> <td style="border: 1px solid black; padding: 0.75em; background-color: #ffaaaa;">1 </td> <td style="border: 1px solid black; padding: 0.75em;">0 </td></tr></tbody></table> </td> <td><span typeof="mw:File"><a href="/wiki/Fichier:Venn0110.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Venn0110.svg/100px-Venn0110.svg.png" decoding="async" width="100" height="73" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Venn0110.svg/150px-Venn0110.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Venn0110.svg/200px-Venn0110.svg.png 2x" data-file-width="410" data-file-height="299" /></a></span> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Logiques_non_classiques">Logiques non classiques</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Connecteur_logique&veaction=edit&section=4" title="Modifier la section : Logiques non classiques" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Connecteur_logique&action=edit&section=4" title="Modifier le code source de la section : Logiques non classiques"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Logique_intuitionniste">Logique intuitionniste</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Connecteur_logique&veaction=edit&section=5" title="Modifier la section : Logique intuitionniste" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Connecteur_logique&action=edit&section=5" title="Modifier le code source de la section : Logique intuitionniste"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone-css loupe">Article détaillé : <a href="/wiki/S%C3%A9mantique_de_Kripke" title="Sémantique de Kripke">sémantique de Kripke</a>.</div></div> <p>Une sémantique possible de la <a href="/wiki/Logique_intuitionniste" title="Logique intuitionniste">logique intuitionniste</a> se fait dans les <a href="/wiki/S%C3%A9mantique_de_Kripke" title="Sémantique de Kripke">modèles de Kripke</a>. Grosso modo, un modèle de Kripke est un graphe étiqueté, dont les nœuds sont appelés des « mondes », les étiquettes sont des formules et la relation sous-jacente <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 R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4b0bfb3769bf24d80e15374dc37b0441e2616e33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}"></span> est dite <i>relation d'accessibilité</i>. Dans ces graphes, la sémantique d'une formule <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 \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span> dont le connecteur principal est <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 c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> est un modèle de Kripke avec un monde étiqueté par la formule <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 \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span>. La sémantique de la formule est définie à partir des sémantiques des composants de la formule. Si la formule <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 \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span> est <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 \psi ~c~\theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> <mtext> </mtext> <mi>c</mi> <mtext> </mtext> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi ~c~\theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff6a93a57bb0a9228decd9a7c97606f091746903" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.772ex; height:2.509ex;" alt="{\displaystyle \psi ~c~\theta }"></span>, la sémantique de <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 \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span> se fera à partir des sémantiques de <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 \psi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ψ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \psi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45e5789e5d9c8f7c79744f43ecaaf8ba42a8553a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.513ex; height:2.509ex;" alt="{\displaystyle \psi }"></span> et <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 \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span>. Dire que dans le modèle de Kripke <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 {\mathcal {M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cc2abebd45ec020509a0ec548b67c9a2cb7cecd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.791ex; height:2.176ex;" alt="{\displaystyle {\mathcal {M}}}"></span>, la formule <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 \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span> étiquette le monde <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 w}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:1.676ex;" alt="{\displaystyle w}"></span>, s'écrit <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 {\mathcal {M}},w\models \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> <mo>,</mo> <mi>w</mi> <mo>⊨</mo> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {M}},w\models \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d66d8b09b0c5f19e49e4fb540c4146baefc01ac2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.179ex; height:2.843ex;" alt="{\displaystyle {\mathcal {M}},w\models \phi }"></span>. Dans ce cas <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 {\mathcal {M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cc2abebd45ec020509a0ec548b67c9a2cb7cecd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.791ex; height:2.176ex;" alt="{\displaystyle {\mathcal {M}}}"></span> <i>est un modèle de</i> <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 \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span>. </p> <div class="mw-heading mw-heading5"><h5 id="Un_exemple">Un exemple</h5><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Connecteur_logique&veaction=edit&section=6" title="Modifier la section : Un exemple" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Connecteur_logique&action=edit&section=6" title="Modifier le code source de la section : Un exemple"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Par exemple, supposons que la formule soit <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 p\Rightarrow q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">⇒</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p\Rightarrow q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66a1178759137a460fdf9377cd24ee749dac8de9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:5.942ex; height:2.176ex;" alt="{\displaystyle p\Rightarrow q}"></span>. Son connecteur principal est <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 \Rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇒</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/469b737d167b9b28a74e27c7f5e35b5ea9256100" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Rightarrow }"></span>. La définition de la sémantique de <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 p\Rightarrow q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">⇒</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p\Rightarrow q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66a1178759137a460fdf9377cd24ee749dac8de9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:5.942ex; height:2.176ex;" alt="{\displaystyle p\Rightarrow q}"></span> fonctionne ainsi : pour pouvoir dire que <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 {\mathcal {M}},w\models p\Rightarrow q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> <mo>,</mo> <mi>w</mi> <mo>⊨</mo> <mi>p</mi> <mo stretchy="false">⇒</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {M}},w\models p\Rightarrow q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/564a52f6d2e53f9745bce1c35b8c40b6fead9324" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.647ex; height:2.843ex;" alt="{\displaystyle {\mathcal {M}},w\models p\Rightarrow q}"></span>, il faut que, dans le modèle <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 {\mathcal {M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2cc2abebd45ec020509a0ec548b67c9a2cb7cecd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.791ex; height:2.176ex;" alt="{\displaystyle {\mathcal {M}}}"></span>, pour tout monde <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 w'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>w</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98af407af5c02e29010c7563af95f8986026679c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.349ex; height:2.509ex;" alt="{\displaystyle w'}"></span>, accessible à partir de <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 w}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle w}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88b1e0c8e1be5ebe69d18a8010676fa42d7961e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.664ex; height:1.676ex;" alt="{\displaystyle w}"></span>, autrement dit tel que <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 wRw'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>w</mi> <mi>R</mi> <msup> <mi>w</mi> <mo>′</mo> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle wRw'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c30412e4c988b8f022b202c72082d4df8343e4b8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.777ex; height:2.509ex;" alt="{\displaystyle wRw'}"></span>, on ait : <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 {\mathcal {M}},w'\models p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> <mo>,</mo> <msup> <mi>w</mi> <mo>′</mo> </msup> <mo>⊨</mo> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {M}},w'\models p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b90a68171bb47c9306405f14a5092696e3999b0f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.648ex; height:3.009ex;" alt="{\displaystyle {\mathcal {M}},w'\models p}"></span> implique <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 {\mathcal {M}},w'\models q}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">M</mi> </mrow> </mrow> <mo>,</mo> <msup> <mi>w</mi> <mo>′</mo> </msup> <mo>⊨</mo> <mi>q</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {M}},w'\models q}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59136e86e6ac6cd798b360805700950f453cd107" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.548ex; height:3.009ex;" alt="{\displaystyle {\mathcal {M}},w'\models q}"></span>. </p> <div class="mw-heading mw-heading4"><h4 id="Logiques_modales">Logiques modales</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Connecteur_logique&veaction=edit&section=7" title="Modifier la section : Logiques modales" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Connecteur_logique&action=edit&section=7" title="Modifier le code source de la section : Logiques modales"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="bandeau-container bandeau-section metadata bandeau-niveau-information"><div class="bandeau-cell bandeau-icone"><span class="mw-valign-text-top noviewer" typeof="mw:File"><a href="/wiki/Fichier:Fairytale_warning.png" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/17px-Fairytale_warning.png" decoding="async" width="17" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/26px-Fairytale_warning.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/34px-Fairytale_warning.png 2x" data-file-width="64" data-file-height="64" /></a></span></div><div class="bandeau-cell">Cette section est vide, insuffisamment détaillée ou incomplète. <a href="/wiki/Sp%C3%A9cial:EditPage/Connecteur_logique" title="Spécial:EditPage/Connecteur logique">Votre aide</a> est la bienvenue ! <a href="/wiki/Aide:Comment_modifier_une_page" title="Aide:Comment modifier une page">Comment faire ?</a></div></div> <p>Il faut dans ce cadre expliquer comment les connecteurs se comportent vis-à-vis des modalités. </p> <div class="mw-heading mw-heading2"><h2 id="Systèmes_complets_de_connecteurs"><span id="Syst.C3.A8mes_complets_de_connecteurs"></span>Systèmes complets de connecteurs</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Connecteur_logique&veaction=edit&section=8" title="Modifier la section : Systèmes complets de connecteurs" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Connecteur_logique&action=edit&section=8" title="Modifier le code source de la section : Systèmes complets de connecteurs"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>En <a href="/wiki/Logique_classique" title="Logique classique">logique classique</a>, avec le <a href="/wiki/Principe_du_tiers_exclu" title="Principe du tiers exclu">tiers exclu</a>, la sémantique est donnée (via le <a href="/wiki/Th%C3%A9or%C3%A8me_de_compl%C3%A9tude_du_calcul_propositionnel" class="mw-redirect" title="Théorème de complétude du calcul propositionnel">théorème de complétude du calcul propositionnel</a>) par les <a href="/wiki/Table_de_v%C3%A9rit%C3%A9" title="Table de vérité">tables de vérité</a>. </p><p>Une logique p-valente possède <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 p^{(p^{n})}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p^{(p^{n})}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32fbd065ba97e660d0b2c983c666d81bfde5aa4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:4.562ex; height:3.176ex;" alt="{\displaystyle p^{(p^{n})}}"></span> connecteurs n-aires. Cela correspond aux nombres de formules distinctes (c'est-à-dire deux à deux non équivalentes) que l'on peut écrire avec n propositions atomiques distinctes (p<sub>1</sub>, p<sub>2</sub>, ... p<sub>n</sub>) dans une logique p-valente. </p><p>La logique bivalente usuelle a donc <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 2^{(2^{n})}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2^{(2^{n})}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c85ace2cf51267ac1a21bb49e6d32307f7ef2d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.461ex; height:2.843ex;" alt="{\displaystyle 2^{(2^{n})}}"></span> connecteurs n-aires. </p><p>Ces logiques ont donc une infinité de connecteurs, pris indépendamment de leur <a href="/wiki/Arit%C3%A9" title="Arité">arité</a>. </p><p>On appelle « système complet de connecteur » un ensemble de connecteurs d'une logique qui suffit à définir tous les autres<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite_crochet">[</span>3<span class="cite_crochet">]</span></a></sup>. </p><p>Pour la logique propositionnel classique, les connecteurs usuels que sont la négation, la conjonction, la disjonction, l'implication et l'équivalence forment ensemble un système complet de connecteurs. </p><p>On démontre, via les notions de <a href="/wiki/Forme_normale_conjonctive" title="Forme normale conjonctive">forme normale conjonctive</a> et <a href="/wiki/Forme_normale_disjonctive" title="Forme normale disjonctive">forme normale disjonctive</a>, que {négation, conjonction, disjonction}, ensemble de connecteurs au plus binaires, est un système complet de connecteurs pour la logique propositionnelle classique. Pour exemple : <i>P</i> ⇒ <i>Q</i> équivaut à ¬<i>P</i> <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 \lor }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lor }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab47f6b1f589aedcf14638df1d63049d233d851a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \lor }"></span> <i>Q</i> (lire <i>non(P) ou Q</i>). </p><p>La généralisation à des logiques classiques p-valentes a été faite par <a href="/wiki/Emil_Post" title="Emil Post">Emil Post</a> en 1921 dans <i>Introduction à une théorie générale des propositions élémentaires</i>. Il montre qu'avec un connecteur unaire qui fait une <a href="/wiki/Permutation_circulaire" title="Permutation circulaire">permutation circulaire</a> sur les p valeurs de vérité (qui peuvent être notées 0, 1, 2, ... p-1) et qu'avec deux connecteurs binaires, l'un prenant le <i>max</i> de deux valeurs de vérité et l'autre le <i>min</i> de deux valeurs de vérité, on peut écrire toute formule de calcul propositionnel. </p><p>Dans le cas de la logique bivalente classique, l'infinité des connecteurs peut être ramené à un seul, binaire. Parmi les 16 connecteurs binaires, deux sont des systèmes complets de connecteurs, les deux <a href="/wiki/Barre_de_Sheffer" title="Barre de Sheffer">barres de Sheffer</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Notes_et_références"><span id="Notes_et_r.C3.A9f.C3.A9rences"></span>Notes et références</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Connecteur_logique&veaction=edit&section=9" title="Modifier la section : Notes et références" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Connecteur_logique&action=edit&section=9" title="Modifier le code source de la section : Notes et références"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small decimal" style=""><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink noprint"><a href="#cite_ref-1">↑</a> </span><span class="reference-text">Par exemple la règle du <a href="/wiki/Tiers_exclu" class="mw-redirect" title="Tiers exclu">tiers exclu</a> est ou non satisfaite.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink noprint"><a href="#cite_ref-2">↑</a> </span><span class="reference-text">Une logique <a href="/wiki/Logique_polyvalente" title="Logique polyvalente">p-valente</a> possède <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 p^{(p^{n})}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">(</mo> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p^{(p^{n})}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32fbd065ba97e660d0b2c983c666d81bfde5aa4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:4.562ex; height:3.176ex;" alt="{\displaystyle p^{(p^{n})}}"></span> connecteurs n-aires.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink noprint"><a href="#cite_ref-3">↑</a> </span><span class="reference-text">La logique intuitionniste n'a pas de système complet de connecteurs.</span> </li> </ol></div> </div> <div class="navbox-container" style="clear:both;"> <table class="navbox collapsible noprint autocollapse" style=""> <tbody><tr><th class="navbox-title" colspan="3" style=""><div style="float:left; width:6em; text-align:left"><div class="noprint plainlinks nowrap tnavbar" style="padding:0; font-size:xx-small; color:var(--color-emphasized, #000000);"><a href="/wiki/Mod%C3%A8le:Palette_Connecteurs_logiques" title="Modèle:Palette Connecteurs logiques"><abbr class="abbr" title="Voir ce modèle.">v</abbr></a> · <a class="external text" href="https://fr.wikipedia.org/w/index.php?title=Mod%C3%A8le:Palette_Connecteurs_logiques&action=edit"><abbr class="abbr" title="Modifier ce modèle. Merci de prévisualiser avant de sauvegarder.">m</abbr></a></div></div><div style="font-size:110%"><a class="mw-selflink selflink">Connecteurs logiques</a></div></th> </tr> <tr> <td class="navbox-list" style="text-align:center;" colspan="2"><a href="/wiki/Tautologie_(logique)" title="Tautologie (logique)">Tautologie</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 \top }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">⊤</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \top }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf12e436fef2365e76fcb1034a51179d8328bb33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \top }"></span></td> <td class="navbox-image" rowspan="5" style="vertical-align:middle;padding-left:7px"><span typeof="mw:File"><a href="/wiki/Fichier:Logical_connectives_Hasse_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/80px-Logical_connectives_Hasse_diagram.svg.png" decoding="async" width="80" height="113" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/120px-Logical_connectives_Hasse_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/160px-Logical_connectives_Hasse_diagram.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></td> </tr> <tr> <td class="navbox-list navbox-even" style="text-align:center;" colspan="2"><div class="liste-horizontale"> <ul><li><a href="/wiki/Barre_de_Sheffer" title="Barre de Sheffer">NON-ET</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 \uparrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↑</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \uparrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddb20b28c74cdaa09e1f101d426441da1996072f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.162ex; height:2.509ex;" alt="{\displaystyle \uparrow }"></span></li> <li><a href="/wiki/Implication_r%C3%A9ciproque" title="Implication réciproque">Implication réciproque</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 \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">←</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c0fb4bce772117bbaf55b7ca1539ceff9ae218c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftarrow }"></span></li> <li><a href="/wiki/Implication_(logique)" title="Implication (logique)">Implication</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 \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53e574cc3aa5b4bf5f3f5906caf121a378eef08b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \rightarrow }"></span></li> <li><a href="/wiki/Disjonction_logique" title="Disjonction logique">OU</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 \lor }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lor }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab47f6b1f589aedcf14638df1d63049d233d851a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \lor }"></span></li></ul> </div></td> </tr> <tr> <td class="navbox-list" style="text-align:center;" colspan="2"><div class="liste-horizontale"> <ul><li><a href="/wiki/N%C3%A9gation_logique" title="Négation logique">Négation</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 \neg }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neg }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa78fd02085d39aa58c9e47a6d4033ce41e02fad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.204ex; margin-bottom: -0.376ex; width:1.55ex; height:1.176ex;" alt="{\displaystyle \neg }"></span></li> <li><a href="/wiki/Fonction_OU_exclusif" title="Fonction OU exclusif">XOR</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 \oplus }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊕</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oplus }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b16e2bdaefee9eed86d866e6eba3ac47c710f60" 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 \oplus }"></span></li> <li><a href="/wiki/%C3%89quivalence_logique" title="Équivalence logique">Équivalence</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 \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/046b918c43e05caf6624fe9b676c69ec9cd6b892" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftrightarrow }"></span></li></ul> </div></td> </tr> <tr> <td class="navbox-list navbox-even" style="text-align:center;" colspan="2"><div class="liste-horizontale"> <ul><li><a href="/wiki/Fonction_NON-OU" title="Fonction NON-OU">NON-OU</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 \downarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↓</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \downarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4618f22b0f780805eb94bb407578d9bc9487947a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.162ex; height:2.509ex;" alt="{\displaystyle \downarrow }"></span></li> <li><a href="/wiki/Non-implication" title="Non-implication">Non-implication</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 \nrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↛</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c458d67617e028ed10948d2dbcfef80e9e060a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \nrightarrow }"></span></li> <li><a href="/wiki/Non-implication_r%C3%A9ciproque" title="Non-implication réciproque">Non-implication réciproque</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 \nleftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↚</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nleftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7694c9fc8eebe8a57c8156dd3c2caf022a619439" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \nleftarrow }"></span></li> <li><a href="/wiki/Conjonction_logique" title="Conjonction logique">ET</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 \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span></li></ul> </div></td> </tr> <tr> <td class="navbox-list" style="text-align:center;" colspan="2"><a href="/wiki/Contradiction" title="Contradiction">Contradiction</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 \bot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">⊥</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f282c7bc331cc3bfcf1c57f1452cc23c022f58de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \bot }"></span></td> </tr> </tbody></table> </div> <ul id="bandeau-portail" class="bandeau-portail"><li><span class="bandeau-portail-element"><span class="bandeau-portail-icone"><span class="noviewer skin-invert-image" typeof="mw:File"><a href="/wiki/Portail:Logique" title="Portail de la logique"><img alt="icône décorative" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Logic.svg/48px-Logic.svg.png" decoding="async" width="48" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Logic.svg/72px-Logic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Logic.svg/96px-Logic.svg.png 2x" data-file-width="85" data-file-height="28" /></a></span></span> <span class="bandeau-portail-texte"><a href="/wiki/Portail:Logique" title="Portail:Logique">Portail de la logique</a></span> </span></li> <li><span class="bandeau-portail-element"><span class="bandeau-portail-icone"><span class="noviewer skin-invert-image" typeof="mw:File"><a href="/wiki/Portail:Informatique_th%C3%A9orique" title="Portail de l'informatique théorique"><img alt="icône décorative" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Max-cut.svg/30px-Max-cut.svg.png" decoding="async" width="30" height="24" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Max-cut.svg/45px-Max-cut.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cf/Max-cut.svg/60px-Max-cut.svg.png 2x" data-file-width="200" data-file-height="160" /></a></span></span> <span class="bandeau-portail-texte"><a href="/wiki/Portail:Informatique_th%C3%A9orique" title="Portail:Informatique théorique">Portail de l'informatique théorique</a></span> </span></li> </ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; 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