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<div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Webbplats"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Innehåll" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Innehåll</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">flytta till sidofältet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">dölj</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Inledning</div> </a> </li> <li id="toc-Notation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notation"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Notation</span> </div> </a> <ul id="toc-Notation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Negation_av_implikation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Negation_av_implikation"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Negation av implikation</span> </div> </a> <ul id="toc-Negation_av_implikation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Materiell_implikation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Materiell_implikation"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Materiell implikation</span> </div> </a> <ul id="toc-Materiell_implikation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Materiell_implikation_i_Boolesk_algebra" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Materiell_implikation_i_Boolesk_algebra"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Materiell implikation i Boolesk algebra</span> </div> </a> <ul id="toc-Materiell_implikation_i_Boolesk_algebra-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Implikation_i_första_ordningens_logik" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Implikation_i_första_ordningens_logik"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Implikation i första ordningens logik</span> </div> </a> <ul id="toc-Implikation_i_första_ordningens_logik-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Strikt_implikation" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Strikt_implikation"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Strikt implikation</span> </div> </a> <ul id="toc-Strikt_implikation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kausalitet" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kausalitet"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Kausalitet</span> </div> </a> <ul id="toc-Kausalitet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tekniska_lösningar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tekniska_lösningar"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Tekniska lösningar</span> </div> </a> <button aria-controls="toc-Tekniska_lösningar-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Växla underavsnittet Tekniska lösningar</span> </button> <ul id="toc-Tekniska_lösningar-sublist" class="vector-toc-list"> <li id="toc-Brytarnät" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Brytarnät"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.1</span> <span>Brytarnät</span> </div> </a> <ul id="toc-Brytarnät-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Grindnät" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Grindnät"> <div class="vector-toc-text"> <span class="vector-toc-numb">8.2</span> <span>Grindnät</span> </div> </a> <ul id="toc-Grindnät-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Se_även" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Se_även"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Se även</span> </div> </a> <ul id="toc-Se_även-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Källor" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Källor"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Källor</span> </div> </a> <button aria-controls="toc-Källor-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Växla underavsnittet Källor</span> </button> <ul id="toc-Källor-sublist" class="vector-toc-list"> <li id="toc-Noter" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Noter"> <div class="vector-toc-text"> <span class="vector-toc-numb">10.1</span> <span>Noter</span> </div> </a> <ul id="toc-Noter-sublist" class="vector-toc-list"> </ul> </li> </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="Innehåll" 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="Växla innehållsförteckningen" > <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">Växla innehållsförteckningen</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">Implikation</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="Gå till en artikel på ett annat språk. Tillgänglig på 38 språk" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-38" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">38 språk</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8C%A5%E1%8C%88%E1%8A%9B_%E1%8A%A0%E1%88%9D%E1%8A%AD%E1%8A%95%E1%8B%AE" title="ጥገኛ አምክንዮ – amhariska" lang="am" hreflang="am" data-title="ጥገኛ አምክንዮ" data-language-autonym="አማርኛ" data-language-local-name="amhariska" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D8%B6%D9%8A%D8%A9_%D8%B4%D8%B1%D8%B7%D9%8A%D8%A9" title="قضية شرطية – arabiska" lang="ar" hreflang="ar" data-title="قضية شرطية" data-language-autonym="العربية" data-language-local-name="arabiska" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%86%D0%BC%D0%BF%D0%BB%D1%96%D0%BA%D0%B0%D1%86%D1%8B%D1%8F" title="Імплікацыя – belarusiska" lang="be" hreflang="be" data-title="Імплікацыя" data-language-autonym="Беларуская" data-language-local-name="belarusiska" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%86%D0%BC%D0%BF%D0%BB%D1%96%D0%BA%D0%B0%D1%86%D1%8B%D1%8F" title="Імплікацыя – belarusiska (tarasjkevitsa)" lang="be-tarask" hreflang="be-tarask" data-title="Імплікацыя" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="belarusiska (tarasjkevitsa)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%98%D0%BC%D0%BF%D0%BB%D0%B8%D0%BA%D0%B0%D1%86%D0%B8%D1%8F" title="Импликация – bulgariska" lang="bg" hreflang="bg" data-title="Импликация" data-language-autonym="Български" data-language-local-name="bulgariska" 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/Condicional_material" title="Condicional material – katalanska" lang="ca" hreflang="ca" data-title="Condicional material" data-language-autonym="Català" data-language-local-name="katalanska" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Implikace" title="Implikace – tjeckiska" lang="cs" hreflang="cs" data-title="Implikace" data-language-autonym="Čeština" data-language-local-name="tjeckiska" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Subjunktion" title="Subjunktion – tyska" lang="de" hreflang="de" data-title="Subjunktion" data-language-autonym="Deutsch" data-language-local-name="tyska" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Implikatsioon" title="Implikatsioon – estniska" lang="et" hreflang="et" data-title="Implikatsioon" data-language-autonym="Eesti" data-language-local-name="estniska" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Material_conditional" title="Material conditional – engelska" lang="en" hreflang="en" data-title="Material conditional" data-language-autonym="English" data-language-local-name="engelska" 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/Condicional_material" title="Condicional material – spanska" lang="es" hreflang="es" data-title="Condicional material" data-language-autonym="Español" data-language-local-name="spanska" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Implico" title="Implico – esperanto" lang="eo" hreflang="eo" data-title="Implico" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B4%D8%B1%D8%B7%DB%8C_%D9%85%D8%A7%D8%AF%DB%8C" title="شرطی مادی – persiska" lang="fa" hreflang="fa" data-title="شرطی مادی" data-language-autonym="فارسی" data-language-local-name="persiska" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Implication_(logique)" title="Implication (logique) – franska" lang="fr" hreflang="fr" data-title="Implication (logique)" data-language-autonym="Français" data-language-local-name="franska" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BB%D5%B4%D5%BA%D5%AC%D5%AB%D5%AF%D5%A1%D6%81%D5%AB%D5%A1" title="Իմպլիկացիա – armeniska" lang="hy" hreflang="hy" data-title="Իմպլիկացիա" data-language-autonym="Հայերեն" data-language-local-name="armeniska" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Implikacija" title="Implikacija – kroatiska" lang="hr" hreflang="hr" data-title="Implikacija" data-language-autonym="Hrvatski" data-language-local-name="kroatiska" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Implicazione_logica" title="Implicazione logica – italienska" lang="it" hreflang="it" data-title="Implicazione logica" data-language-autonym="Italiano" data-language-local-name="italienska" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%9D-%D7%90%D7%96" title="אם-אז – hebreiska" lang="he" hreflang="he" data-title="אם-אז" data-language-autonym="עברית" data-language-local-name="hebreiska" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%98%D0%BC%D0%BF%D0%BB%D0%B8%D0%BA%D0%B0%D1%86%D0%B8%D1%8F" title="Импликация – kazakiska" lang="kk" hreflang="kk" data-title="Импликация" data-language-autonym="Қазақша" data-language-local-name="kazakiska" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Implik%C3%A1ci%C3%B3" title="Implikáció – ungerska" lang="hu" hreflang="hu" data-title="Implikáció" data-language-autonym="Magyar" data-language-local-name="ungerska" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D1%80%D0%B8%D1%98%D0%B0%D0%BB%D0%BD%D0%B0_%D0%B8%D0%BC%D0%BF%D0%BB%D0%B8%D0%BA%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Материјална импликација – makedonska" lang="mk" hreflang="mk" data-title="Материјална импликација" data-language-autonym="Македонски" data-language-local-name="makedonska" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Logische_implicatie" title="Logische implicatie – nederländska" lang="nl" hreflang="nl" data-title="Logische implicatie" data-language-autonym="Nederlands" data-language-local-name="nederländska" class="interlanguage-link-target"><span>Nederlands</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%E5%8C%85%E5%90%AB" title="論理包含 – japanska" lang="ja" hreflang="ja" data-title="論理包含" data-language-autonym="日本語" data-language-local-name="japanska" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Subjunksjon_(logikk)" title="Subjunksjon (logikk) – norskt bokmål" lang="nb" hreflang="nb" data-title="Subjunksjon (logikk)" data-language-autonym="Norsk bokmål" data-language-local-name="norskt bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Amplicassion" title="Amplicassion – piemontesiska" lang="pms" hreflang="pms" data-title="Amplicassion" data-language-autonym="Piemontèis" data-language-local-name="piemontesiska" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Implikacja_materialna" title="Implikacja materialna – polska" lang="pl" hreflang="pl" data-title="Implikacja materialna" data-language-autonym="Polski" data-language-local-name="polska" 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/Condicional_material" title="Condicional material – portugisiska" lang="pt" hreflang="pt" data-title="Condicional material" data-language-autonym="Português" data-language-local-name="portugisiska" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Implikaciya" title="Implikaciya – karakalpakiska" lang="kaa" hreflang="kaa" data-title="Implikaciya" data-language-autonym="Qaraqalpaqsha" data-language-local-name="karakalpakiska" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Implica%C8%9Bie_logic%C4%83" title="Implicație logică – rumänska" lang="ro" hreflang="ro" data-title="Implicație logică" data-language-autonym="Română" data-language-local-name="rumänska" 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%98%D0%BC%D0%BF%D0%BB%D0%B8%D0%BA%D0%B0%D1%86%D0%B8%D1%8F" title="Импликация – ryska" lang="ru" hreflang="ru" data-title="Импликация" data-language-autonym="Русский" data-language-local-name="ryska" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Implication_(logic)" title="Implication (logic) – Simple English" lang="en-simple" hreflang="en-simple" data-title="Implication (logic)" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Implik%C3%A1cia" title="Implikácia – slovakiska" lang="sk" hreflang="sk" data-title="Implikácia" data-language-autonym="Slovenčina" data-language-local-name="slovakiska" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Implikaatio" title="Implikaatio – finska" lang="fi" hreflang="fi" data-title="Implikaatio" data-language-autonym="Suomi" data-language-local-name="finska" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Implikasyon" title="Implikasyon – tagalog" lang="tl" hreflang="tl" data-title="Implikasyon" data-language-autonym="Tagalog" data-language-local-name="tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%98%D0%BC%D0%BF%D0%BB%D0%B8%D0%BA%D0%B0%D1%86%D0%B8%D1%8F" title="Импликация – tatariska" lang="tt" hreflang="tt" data-title="Импликация" data-language-autonym="Татарча / tatarça" data-language-local-name="tatariska" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%87%E0%B8%B7%E0%B9%88%E0%B8%AD%E0%B8%99%E0%B9%84%E0%B8%82%E0%B9%80%E0%B8%8A%E0%B8%B4%E0%B8%87%E0%B8%95%E0%B8%A3%E0%B8%A3%E0%B8%81%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="เงื่อนไขเชิงตรรกศาสตร์ – thailändska" lang="th" hreflang="th" data-title="เงื่อนไขเชิงตรรกศาสตร์" data-language-autonym="ไทย" data-language-local-name="thailändska" class="interlanguage-link-target"><span>ไทย</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%B0_%D1%96%D0%BC%D0%BF%D0%BB%D1%96%D0%BA%D0%B0%D1%86%D1%96%D1%8F" title="Логічна імплікація – ukrainska" lang="uk" hreflang="uk" data-title="Логічна імплікація" data-language-autonym="Українська" 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vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Utseende</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">flytta till sidofältet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">dölj</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Från Wikipedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sv" dir="ltr"><dl><dd><i>Uppslagsorden ”⇒” och ”⇐” leder hit. För andra betydelser, se <a href="/wiki/%E2%86%92" class="mw-disambig" title="→">→</a> och <a href="/wiki/%E2%86%90" class="mw-redirect" title="←">←</a>. För pil som grafisk symbol, se <a href="/wiki/Pil_(figur)" title="Pil (figur)">Pil (figur)</a>.</i></dd></dl> <style data-mw-deduplicate="TemplateStyles:r53696904">.mw-parser-output .infobox{border:1px solid #aaa;background-color:#f9f9f9;color:black;margin:.5em 0 .5em 1em;padding:.2em;float:right;clear:right;width:22em;text-align:left;font-size:88%;line-height:1.6em}.mw-parser-output .infobox td,.mw-parser-output .infobox th{vertical-align:top;padding:0 .2em}.mw-parser-output .infobox caption{font-size:larger}.mw-parser-output .infobox.bordered{border-collapse:collapse}.mw-parser-output .infobox.bordered td,.mw-parser-output .infobox.bordered th{border:1px solid #aaa}.mw-parser-output .infobox.bordered .borderless td,.mw-parser-output .infobox.bordered .borderless th{border:0}.mw-parser-output .infobox-showbutton button,.mw-parser-output .infobox-showbutton .mw-collapsible-text{color:inherit}.mw-parser-output .infobox.bordered .mergedtoprow td,.mw-parser-output .infobox.bordered .mergedtoprow th{border:0;border-top:1px solid #aaa;border-right:1px solid #aaa}.mw-parser-output .infobox.bordered .mergedrow td,.mw-parser-output .infobox.bordered .mergedrow th{border:0;border-right:1px solid #aaa}.mw-parser-output .infobox.geography{border:1px solid #ccd2d9;text-align:left;border-collapse:collapse;line-height:1.2em;font-size:90%}.mw-parser-output .infobox.geography td,.mw-parser-output .infobox.geography th{border-top:solid 1px #ccd2d9;padding:0.4em 0.6em 0.4em 0.6em}.mw-parser-output .infobox.geography .mergedtoprow td,.mw-parser-output .infobox.geography .mergedtoprow th{border-top:solid 1px #ccd2d9;padding:0.4em 0.6em 0.2em 0.6em}.mw-parser-output .infobox.geography .mergedrow td,.mw-parser-output .infobox.geography .mergedrow th{border:0;padding:0 0.6em 0.2em 0.6em}.mw-parser-output .infobox.geography .mergedbottomrow td,.mw-parser-output .infobox.geography .mergedbottomrow th{border-top:0;border-bottom:solid 1px #ccd2d9;padding:0 0.6em 0.4em 0.6em}.mw-parser-output .infobox.geography .maptable td,.mw-parser-output .infobox.geography .maptable th{border:0;padding:0}</style> <table class="infobox"> <tbody><tr> <th><span typeof="mw:File"><a href="/wiki/Fil:AND_ANSI.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/AND_ANSI.svg/35px-AND_ANSI.svg.png" decoding="async" width="35" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/AND_ANSI.svg/53px-AND_ANSI.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/AND_ANSI.svg/70px-AND_ANSI.svg.png 2x" data-file-width="100" data-file-height="50" /></a></span> </th></tr> <tr> <th style="background:#ddddff;" width="200px"> <a href="/wiki/Logisk_operator" title="Logisk operator">Logisk operator</a> (<a href="/wiki/Logisk_grind" title="Logisk grind">Logisk grind</a>)  </th></tr> <tr> <td> <ul><li><a href="/wiki/Negation" title="Negation">Negation</a> (<a href="/wiki/NOT" class="mw-redirect" title="NOT">NOT</a>)</li> <li><a href="/wiki/Konjunktion_(logik)" title="Konjunktion (logik)">Konjunktion</a> (<a href="/wiki/Och" class="mw-redirect" title="Och">AND</a>, <a href="/wiki/NAND" title="NAND">NAND</a>)</li> <li><a href="/wiki/Disjunktion" title="Disjunktion">Disjunktion</a> (<a href="/wiki/OR_(logisk_funktion)" class="mw-redirect" title="OR (logisk funktion)">OR</a>, <a href="/wiki/XOR" class="mw-redirect" title="XOR">XOR</a>, <a href="/wiki/NOR" title="NOR">NOR</a>)</li> <li><a class="mw-selflink selflink">Implikation</a></li> <li><a href="/wiki/Ekvivalens_(logik)" title="Ekvivalens (logik)">Ekvivalens</a> (<a href="/wiki/XNOR" title="XNOR">XNOR</a>)</li></ul> </td></tr> <tr> <th style="background:#ddddff;" width="200px">Se även </th></tr> <tr> <td> <ul><li><a href="/wiki/Logisk_operator" title="Logisk operator">Logisk operator</a> (konnektiv)</li> <li><a href="/wiki/Sanningsfunktion" title="Sanningsfunktion">Sanningsfunktion</a></li> <li><a href="/wiki/Sanningsv%C3%A4rdetabell" title="Sanningsvärdetabell">Sanningsvärdetabell</a></li> <li><a href="/wiki/De_Morgans_lagar" title="De Morgans lagar">De Morgans lagar</a></li></ul> </td></tr> <tr> <td><div class="noprint plainlinks" style="background-color:transparent; padding:0; white-space:nowrap; font-weight:normal; font-size:80%; ; color: inherit;">Denna tabell: <a href="/wiki/Mall:Logiska_funktioner" title="Mall:Logiska funktioner"><span title="Visa denna mall" style=";">visa</span></a> <span style="font-size:80%;">•</span> <a class="external text" href="https://sv.wikipedia.org/w/index.php?title=Mall:Logiska_funktioner&action=edit"><span style=";" title="Redigera den här mallen">redigera</span></a></div> </td></tr></tbody></table> <p>En <b>implikation</b> eller <b>villkorssats</b> är en <a href="/wiki/Sats_(matematik)" class="mw-redirect" title="Sats (matematik)">sats</a> på formen "om <i>A</i> så <i>B</i>", där A och B var för sig är satser. Implikationens första del ("villkoret") kallas <a href="/wiki/Antecedent" title="Antecedent">antecedent</a> och dess andra del ("slutsatsen") kallas <a href="/wiki/Konsekvent" title="Konsekvent">konsekvent</a>. En <b>implikation</b> kan vara <a href="/wiki/Satslogik" title="Satslogik">materiell</a>, <a href="/wiki/Tautologi_(logik)" title="Tautologi (logik)">tautolog</a>, formell eller <a href="/wiki/Kontrafaktisk_villkorssats" title="Kontrafaktisk villkorssats">kontrafaktisk</a>. </p> <ul><li><a href="/wiki/Materiell_implikation" title="Materiell implikation">Materiell implikation</a>: <i>p</i> → <i>q</i> är falsk om <i>p</i> är sann och <i>q</i> är falsk och sann i övriga fall.</li> <li><a href="/wiki/Tautolog_implikation" title="Tautolog implikation">Tautolog implikation</a>: <i>F</i> → <i>G</i> är sann för alla värden på de i formlerna <i>F</i> och <i>G</i> ingående variablerna.</li> <li>Formell implikation eller vardagsspråklig implikation: <i>A</i> → <i>B</i>, där ett visst kausalt eller formellt, ej väldefinierat, samband måste föreligga mellan försats och eftersats för att implikationen skall betraktas som meningsfull och sann.</li> <li><a href="/wiki/Kontrafaktisk_villkorssats" title="Kontrafaktisk villkorssats">Kontrafaktisk implikation</a>: En sats av typen "om <i>A</i> vore - vilket <i>A</i> inte är - så vore <i>B</i>" eller "om <i>A</i> inte vore - vilket <i>A</i> är - så vore <i>B</i>".</li></ul> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Notation">Notation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Implikation&veaction=edit&section=1" title="Redigera avsnitt: Notation" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Implikation&action=edit&section=1" title="Redigera avsnitts källkod: Notation"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Inom logiken betecknas implikation med <b>→</b>. För att inte förväxla denna pil med <a href="/wiki/Gr%C3%A4nsv%C3%A4rde" title="Gränsvärde">gränsvärdespilen</a> använder man istället, inom <a href="/wiki/Matematik" title="Matematik">matematiken</a>, oftast den dubbelstreckade pilen <b>⇒</b>. På motsvarande sätt används dubbelpilen för <a href="/wiki/Ekvivalens_(logik)" title="Ekvivalens (logik)">ekvivalens</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Negation_av_implikation">Negation av implikation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Implikation&veaction=edit&section=2" title="Redigera avsnitt: Negation av implikation" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Implikation&action=edit&section=2" title="Redigera avsnitts källkod: Negation av implikation"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I det naturliga språket finns ett flertal skilda betydelser av "om <i>A</i> så <i>B</i>": En av dessa är ett uttalande om <i>B</i>, givet att <i>A</i> är uppfyllt. En annan är ett uttalande om att det råder ett villkorsförhållande mellan <i>A</i> och <i>B</i>, det vill säga att det är sant att: "om <i>A</i> så <i>B</i>". Nedan följer ett försök till förklaring av skillnaden mellan dessas betydelser, genom att de två satserna på olika sätt negeras. </p> <ol><li>"Det är <i>inte</i> så att: om Kalle kommer till festen så kommer även Lisa" = "Det är så att: om Kalle kommer till festen så kommer <i>inte</i> Lisa". Detta är ett uttalande om huruvida Lisa kommer eller inte, givet att Kalle kommer.</li> <li>"Det är <i>inte</i> sant att: om Kalle kommer till festen så kommer även Lisa" = "Det är <i>falskt</i> att: om Kalle kommer till festen så kommer även Lisa". Detta är ett uttalande om huruvida implikationen är sann eller inte.</li></ol> <p>Negation av implikation kan uttryckas om <i>A</i> ⇏ <i>B</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Materiell_implikation">Materiell implikation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Implikation&veaction=edit&section=3" title="Redigera avsnitt: Materiell implikation" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Implikation&action=edit&section=3" title="Redigera avsnitts källkod: Materiell implikation"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="noprint huvudartikel" style="font-style:italic;"> <dl><dd>Huvudartikel: <a href="/wiki/Materiell_implikation" title="Materiell implikation">Materiell implikation</a></dd></dl></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:MI-logical.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/MI-logical.png/250px-MI-logical.png" decoding="async" width="250" height="203" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/MI-logical.png/375px-MI-logical.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/MI-logical.png/500px-MI-logical.png 2x" data-file-width="737" data-file-height="599" /></a><figcaption><a href="/wiki/Venndiagram" title="Venndiagram">Venndiagram</a> för <i>A</i> → <i>B</i></figcaption></figure> <p><a href="/wiki/Materiell_implikation" title="Materiell implikation">Materiell implikation</a> betecknas vanligen med <b>→</b> eller <b>⊃</b>. Den definieras i satslogiken som en funktion av de ingående påståendenas <a href="/wiki/Satslogik" title="Satslogik">sanningsvärden</a>. Satsen <i>p → q</i> är falsk endast om <i>p</i> är sann och <i>q</i> är falsk. <i>p</i> → <i>q</i> kan skrivas som ¬<i>p</i> ∨ <i>q</i> (<a href="/wiki/Klausul" title="Klausul">klausul</a>) och har följande <a href="/wiki/Sanningstabell" class="mw-redirect" title="Sanningstabell">sanningstabell</a>, där S står för sann och f för falsk: </p> <table border="0" cellspacing="5" cellpadding="6" rules="all" frame="box" style="border:2px solid #777; background:#ffffff; margin:0 0 .5em 3em; line-height: 90%; text-align:center; border-collapse:collapse;"> <tbody><tr style="background:#eeeeff; margin:0em;"> <td><i>p</i></td> <td><i>q</i></td> <td><i>p</i> → <i>q</i></td> <td>¬<i>p</i> ∨ <i>q</i> </td></tr> <tr> <td>S</td> <td>S</td> <td>S</td> <td>S </td></tr> <tr> <td>S</td> <td>F</td> <td>F</td> <td>F </td></tr> <tr> <td>F</td> <td>S</td> <td>S</td> <td>S </td></tr> <tr> <td>F</td> <td>F</td> <td>S</td> <td>S </td></tr></tbody></table> <p>Att en sats materiellt implicerar en annan, betyder endast att det icke är så, att den första satsen är sann och den andra falsk. </p><p>Vissa egenskaper hos den materiella implikationen ger upphov till <a href="/wiki/Paradox" title="Paradox">paradoxala</a> resultat. Dessa sammanfattas under benämningen <a href="/wiki/Implikationsparadoxer" title="Implikationsparadoxer">implikationsparadoxer</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Materiell_implikation_i_Boolesk_algebra">Materiell implikation i Boolesk algebra</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Implikation&veaction=edit&section=4" title="Redigera avsnitt: Materiell implikation i Boolesk algebra" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Implikation&action=edit&section=4" title="Redigera avsnitts källkod: Materiell implikation i Boolesk algebra"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I <a href="/wiki/Boolesk_algebra" title="Boolesk algebra">Boolesk algebra</a>, där 0 + 1 = 1, 1 + 1 = 1, 0´=1 och 1´= 0, uttrycks materiell implikation, p→q, som p´+ q. </p> <table border="0" cellspacing="5" cellpadding="6" rules="all" frame="box" style="border:2px solid #777; background:#ffffff; margin:0 0 .5em 3em; line-height: 90%; text-align:center; border-collapse:collapse;"> <tbody><tr style="background:#eeeeff; margin:0em;"> <td><i>p</i></td> <td><i>q</i></td> <td><i>p</i> → <i>q</i></td> <td><i>p</i>´+ <i>q</i> </td></tr> <tr> <td>1</td> <td>1</td> <td>1</td> <td>1 </td></tr> <tr> <td>1</td> <td>0</td> <td>0</td> <td>0 </td></tr> <tr> <td>0</td> <td>1</td> <td>1</td> <td>1 </td></tr> <tr> <td>0</td> <td>0</td> <td>1</td> <td>1 </td></tr></tbody></table> <p>Boolesk algebra är <a href="/wiki/Isomorfi" title="Isomorfi">isomorf</a> med <a href="/wiki/Satslogik" title="Satslogik">satslogik</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Implikation_i_första_ordningens_logik"><span id="Implikation_i_f.C3.B6rsta_ordningens_logik"></span>Implikation i första ordningens logik</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Implikation&veaction=edit&section=5" title="Redigera avsnitt: Implikation i första ordningens logik" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Implikation&action=edit&section=5" title="Redigera avsnitts källkod: Implikation i första ordningens logik"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I <a href="/wiki/F%C3%B6rsta_ordningens_logik" title="Första ordningens logik">första ordningens logik</a> (FOL) spelar implikationer en viktig roll, bland annat vid formalisering av <a href="/wiki/Kvantifikator" title="Kvantifikator">kvantifierade</a> påståenden och <a href="/wiki/Syllogism" title="Syllogism">syllogistiska</a> slutledningar. Kvantifierade påståenden kan skrivas om och formaliseras till implikationer. Exempelvis: </p> <ul><li>"Alla hästar har fyra ben." kan skrivas "För alla <i>x</i> gäller: om <i>x</i> är en häst så har <i>x</i> fyra ben." ; formaliserat: ∀<i>x</i>(H<i>x</i> → B<i>x</i>), där ∀ betyder <i>"alla"</i>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Strikt_implikation">Strikt implikation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Implikation&veaction=edit&section=6" title="Redigera avsnitt: Strikt implikation" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Implikation&action=edit&section=6" title="Redigera avsnitts källkod: Strikt implikation"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Den materiella implikationen i klassisk satslogik har till följd tre <a href="/wiki/Tautologi_(logik)" title="Tautologi (logik)">tautologier</a> som i viss mening strider mot våra språkliga intuitioner. "<i>A</i> → (<i>B</i> → <i>A</i>)" säger att om <i>A</i> är fallet, så implicerar vad som helst <i>A</i>. Den andra är "¬<i>A</i> → (<i>A</i> → <i>B</i>)", som säger att om <i>A</i> <i>inte</i> är fallet, så implicerar <i>A</i> vad som helst. Den tredje är "(<i>A</i> → <i>B</i>) ∨ (<i>B</i> → <i>A</i>)", alltså att antingen implicerar <i>A B</i>, eller så implicerar <i>B A</i>, oavsett vad <i>A</i> och <i>B</i> står för. Den amerikanske filosofen <a href="/wiki/Clarence_Irving_Lewis" title="Clarence Irving Lewis">C.I. Lewis</a> påpekade att dessa så kallade <a href="/wiki/Implikationsparadoxer" title="Implikationsparadoxer">implikationsparadoxer</a> måste tolkas som att materiell implikation inte på ett rimligt sätt återger hur villkorssatser i vardagsspråket används. Han försökte lösa problemet genom att införa en starkare form av implikation, <i><a href="/w/index.php?title=Strikt_implikation&action=edit&redlink=1" class="new" title="Strikt implikation [inte skriven än]">strikt implikation</a></i><sup id="cite_ref-NE_1-0" class="reference"><a href="#cite_note-NE-1"><span class="cite-reference-link-bracket">[</span>1<span class="cite-reference-link-bracket">]</span></a></sup>, som uttrycks med "det är <i>nödvändigt</i> att om <i>A</i> så <i>B</i>". Att <i>B</i> <i>måste</i> vara sant om <i>A</i> är det betyder att det måste finnas ett kausalt eller formellt samband mellan <i>A</i> och <i>B</i> för att implikationen ska vara giltig.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-reference-link-bracket">[</span>2<span class="cite-reference-link-bracket">]</span></a></sup> Det räcker inte med att sanningsvärdena hos <i>A</i> och <i>B</i> förhåller sig på ett visst sätt till varandra. <i>B</i> ska också på ett eller annat sätt följa ur <i>A</i>.<sup id="cite_ref-NE_1-1" class="reference"><a href="#cite_note-NE-1"><span class="cite-reference-link-bracket">[</span>1<span class="cite-reference-link-bracket">]</span></a></sup> </p><p>Strikt implikation kan i <a href="/wiki/Modal_logik" class="mw-redirect" title="Modal logik">modallogik</a> definieras med hjälp av nödvändighetsoperatorn (L eller □) som L(<i>A</i> → <i>B</i>) och skrivs ibland "<i>A</i> ⥽ <i>B</i>". </p> <div class="mw-heading mw-heading2"><h2 id="Kausalitet">Kausalitet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Implikation&veaction=edit&section=7" title="Redigera avsnitt: Kausalitet" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Implikation&action=edit&section=7" title="Redigera avsnitts källkod: Kausalitet"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Implikationer kan även uttrycka <a href="/wiki/Kausalitet" title="Kausalitet">kausalitet</a> – orsak och verkan. Denna tillämpning tillhör den <a href="/w/index.php?title=Temporal_logik&action=edit&redlink=1" class="new" title="Temporal logik [inte skriven än]">temporala logiken</a> och är starkare påståenden än materiell. </p> <div class="mw-heading mw-heading2"><h2 id="Tekniska_lösningar"><span id="Tekniska_l.C3.B6sningar"></span>Tekniska lösningar</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Implikation&veaction=edit&section=8" title="Redigera avsnitt: Tekniska lösningar" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Implikation&action=edit&section=8" title="Redigera avsnitts källkod: Tekniska lösningar"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I elektriska kretsar, pneumatik, hydraulik, mekanik etc kan funktioner som motsvarar implikationer realiseras. </p> <div class="mw-heading mw-heading3"><h3 id="Brytarnät"><span id="Brytarn.C3.A4t"></span>Brytarnät</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Implikation&veaction=edit&section=9" title="Redigera avsnitt: Brytarnät" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Implikation&action=edit&section=9" title="Redigera avsnitts källkod: Brytarnät"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/Fil:Logik-materiell-impl.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Logik-materiell-impl.svg/250px-Logik-materiell-impl.svg.png" decoding="async" width="250" height="167" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Logik-materiell-impl.svg/375px-Logik-materiell-impl.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Logik-materiell-impl.svg/500px-Logik-materiell-impl.svg.png 2x" data-file-width="345" data-file-height="230" /></a><figcaption>Strömbrytarkoppling som är analog med materiell implikation</figcaption></figure> <div style="clear:left;"></div> <div class="mw-heading mw-heading3"><h3 id="Grindnät"><span id="Grindn.C3.A4t"></span>Grindnät</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Implikation&veaction=edit&section=10" title="Redigera avsnitt: Grindnät" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Implikation&action=edit&section=10" title="Redigera avsnitts källkod: Grindnät"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Funktionen hos materiell implikation kan realiseras med en <a href="/wiki/OR-grind" class="mw-redirect" title="OR-grind">OR-grind</a> med en <a href="/wiki/NOT-grind" class="mw-redirect" title="NOT-grind">inverterad</a> ingång (H = hög nivå, L = låg nivå): </p> <table> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/Fil:MI-gate.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/MI-gate.png/180px-MI-gate.png" decoding="async" width="180" height="77" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/94/MI-gate.png/270px-MI-gate.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/94/MI-gate.png/360px-MI-gate.png 2x" data-file-width="1198" data-file-height="514" /></a></span> </td> <td> <table border="0" cellspacing="5" cellpadding="6" rules="all" frame="box" style="border:2px solid #777; background:#ffffff; margin:0 0 .5em 3em; line-height: 90%; text-align:center; border-collapse:collapse;"> <tbody><tr style="background:#eeeeff; margin:0em;"> <td><i>A</i></td> <td><i>B</i></td> <td>~<i>A</i></td> <td>~<i>A</i> OR <i>B</i></td> <td><i>Y</i> </td></tr> <tr> <td>H</td> <td>H</td> <td>L</td> <td>H</td> <td>H </td></tr> <tr> <td>H</td> <td>L</td> <td>L</td> <td>L</td> <td>L </td></tr> <tr> <td>L</td> <td>H</td> <td>H</td> <td>H</td> <td>H </td></tr> <tr> <td>L</td> <td>L</td> <td>H</td> <td>H</td> <td>H </td></tr></tbody></table> </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Se_även"><span id="Se_.C3.A4ven"></span>Se även</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Implikation&veaction=edit&section=11" title="Redigera avsnitt: Se även" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Implikation&action=edit&section=11" title="Redigera avsnitts källkod: Se även"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Hypotes" title="Hypotes">Hypotes</a></li> <li><a href="/wiki/Implikationsparadoxer" title="Implikationsparadoxer">Implikationsparadoxer</a></li> <li><a href="/wiki/Medf%C3%B6r_(logik)" title="Medför (logik)">Medför (logik)</a></li> <li><a href="/wiki/Tautolog_implikation" title="Tautolog implikation">Tautolog implikation</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Källor"><span id="K.C3.A4llor"></span>Källor</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Implikation&veaction=edit&section=12" title="Redigera avsnitt: Källor" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Implikation&action=edit&section=12" title="Redigera avsnitts källkod: Källor"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Geoffrey Hunter, Metalogic An Introduction to the Metatheory of Standard First-Order Logic, MacMillan London 1971.</li> <li>Göran Hermeren, Logik, Studentlitteratur, Lund 1971.</li> <li>P. Suppes, Introduction to Logic, Van Nostrand, New York 1957.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Noter">Noter</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Implikation&veaction=edit&section=13" title="Redigera avsnitt: Noter" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Implikation&action=edit&section=13" title="Redigera avsnitts källkod: Noter"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-NE-1">^ [<a href="#cite_ref-NE_1-0"><small>a</small></a> <a href="#cite_ref-NE_1-1"><small>b</small></a>] <span class="reference-text"> <a rel="nofollow" class="external text" href="https://www.ne.se/implikation"><i>implikation</i></a> i <i><a href="/wiki/Nationalencyklopedin" title="Nationalencyklopedin">Nationalencyklopedins</a></i> . </span> </li> <li id="cite_note-2"><a href="#cite_ref-2">^</a> <span class="reference-text"><cite style="font-style:normal" class="book" id="CITEREFLübcke,_Poul1988">Lübcke, Poul, red (1988). <i><span>Filosofilexikonet</span></i>. Stockholm. sid. 372. <a href="/wiki/Special:Bokk%C3%A4llor/91-37-10062-9" title="Special:Bokkällor/91-37-10062-9">ISBN 91-37-10062-9</a></cite><span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Filosofilexikonet&rft.date=1988&rft.pages=sid.%26nbsp%3B372&rft.place=Stockholm&rft.isbn=91-37-10062-9&rfr_id=info:sid/en.wikipedia.org:Implikation"><span style="display: none;"> </span></span></span> </li> </ol></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Hämtad från ”<a dir="ltr" href="https://sv.wikipedia.org/w/index.php?title=Implikation&oldid=54190729">https://sv.wikipedia.org/w/index.php?title=Implikation&oldid=54190729</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Wikipedia:Kategorier" title="Wikipedia:Kategorier">Kategorier</a>: <ul><li><a href="/wiki/Kategori:Logik" title="Kategori:Logik">Logik</a></li><li><a href="/wiki/Kategori:Logiska_operatorer" title="Kategori:Logiska operatorer">Logiska operatorer</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Sidan redigerades senast den 5 december 2023 kl. 15.06.</li> <li id="footer-info-copyright">Wikipedias text är tillgänglig under licensen <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.sv">Creative Commons Erkännande-dela-lika 4.0 Unported</a>. 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