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<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Junktor</span></h1>

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<p>Ein <b>Junktor</b> (von <a href="Latein" title="Latein">lat.</a> <i>iungere</i> „verknüpfen, verbinden“) ist eine <a href="Logische_Verkn%C3%BCpfung" title="Logische Verknüpfung">logische Verknüpfung</a> zwischen Aussagen innerhalb der <a href="Aussagenlogik" title="Aussagenlogik">Aussagenlogik</a>, also ein logischer <a href="Operator_(Mathematik)" title="Operator (Mathematik)">Operator</a>. Junktoren werden auch logische Verknüpfungen genannt<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> und als <a href="Logische_Partikel" class="mw-redirect" title="Logische Partikel">logische Partikel</a> klassifiziert.

</p><p>Sprachlich wird zwischen der jeweiligen Verknüpfung selbst (zum Beispiel der <a href="Konjunktion_(Logik)" title="Konjunktion (Logik)">Konjunktion</a>) und dem sie bezeichnenden Wort beziehungsweise Sprachzeichen (zum Beispiel dem Wort „und“ beziehungsweise dem Zeichen „∧“) oft nicht unterschieden.

</p><p>In <a href="Programmiersprache" title="Programmiersprache">Programmiersprachen</a> werden ebenfalls aussagenlogische Junktoren verwendet, die sich aber in wesentlichen Punkten von den üblichen aussagenlogischen Junktoren unterscheiden. Sie werden dort überwiegend als <a href="Logische_Operatoren" class="mw-redirect" title="Logische Operatoren">logische Operatoren</a> bezeichnet.

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<td colspan="3">Übersicht der Junktoren in der Aussagenlogik

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<div class="mw-heading mw-heading2"><h2 id="Aussagenverknüpfung"><span id="Aussagenverkn.C3.BCpfung"></span>Aussagenverknüpfung</h2></div>

<p>In der (formalen) <a href="Logik" title="Logik">Logik</a> bezeichnet man eine Aussage, die mit Hilfe von sprachlichen Partikeln wie „und“, „oder“, „wenn–dann“ und „es ist nicht der Fall, dass“ aus anderen Aussagen zusammengesetzt ist, als <i>komplexe</i> oder <i>zusammengesetzte Aussage</i>, bzw. als <i>Aussagenverknüpfung</i>. Eine Aussage, die <i>nicht</i> aus anderen Aussagen zusammengesetzt ist, wird <a href="Atomare_Aussage" class="mw-redirect" title="Atomare Aussage">atomare Aussage</a> genannt.

</p><p>Beispiel: <i>Wenn</i> Anna Urlaub hat, <i>dann</i> fährt sie ans Meer.

</p><p>In der klassischen Aussagenlogik (vgl. <a href="Klassische_Logik" title="Klassische Logik">klassische Logik</a>) sind die folgenden Junktoren am gebräuchlichsten (bezogen auf zwei Aussagen <span class="mwe-math-element mwe-math-element-inline"><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}">

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<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span> und <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}">

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<annotation encoding="application/x-tex">{\displaystyle Q}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8752c7023b4b3286800fe3238271bbca681219ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" loading="lazy"></span>):<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>

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<ul><li>die <a href="Negation" title="Negation">Negation</a> <span class="mwe-math-element mwe-math-element-inline"><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 P}">

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<annotation encoding="application/x-tex">{\displaystyle \neg P}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5eb0d6c8752f8c7256d69c62e77dfe4c466dbe58.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.296ex; height:2.176ex;" alt="{\displaystyle \neg P}" loading="lazy"></span> entspricht einer Verneinung</li>

<li>die <a href="Konjunktion_(Logik)" title="Konjunktion (Logik)">Konjunktion</a> <span class="mwe-math-element mwe-math-element-inline"><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\land Q}">

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<annotation encoding="application/x-tex">{\displaystyle P\land Q}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c5690bb4822d8c821a00cfe3c6644b046a884af4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.166ex; height:2.509ex;" alt="{\displaystyle P\land Q}" loading="lazy"></span>, das logische Und: „Sowohl P als auch Q“</li>

<li>die <a href="Disjunktion" title="Disjunktion">Disjunktion</a> <span class="mwe-math-element mwe-math-element-inline"><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\vee Q}">

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<annotation encoding="application/x-tex">{\displaystyle P\vee Q}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/57892b87b74754882daffcf850dd8b445b0fc436.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.166ex; height:2.509ex;" alt="{\displaystyle P\vee Q}" loading="lazy"></span>, das einschließende Oder: „Entweder P oder Q oder beide“</li>

<li>die <a href="Implikation" title="Implikation">materiale Implikation</a>, auch Subjunktion oder Konditional genannt, <span class="mwe-math-element mwe-math-element-inline"><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}">

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<annotation encoding="application/x-tex">{\displaystyle P\rightarrow Q}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/86439ea857adc8eaec93c4d14270b8ba6bd2a6a9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.198ex; height:2.509ex;" alt="{\displaystyle P\rightarrow Q}" loading="lazy"></span> beziehungsweise <span class="mwe-math-element mwe-math-element-inline"><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}">

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<annotation encoding="application/x-tex">{\displaystyle P\Rightarrow Q}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/27a57c9bc077d0b20e4f5ec006f5342cfbb18fd2.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.198ex; height:2.509ex;" alt="{\displaystyle P\Rightarrow Q}" loading="lazy"></span>, entspricht der hinreichenden Bedingung „Wenn P, dann Q“</li>

<li>die <a href="Kontravalenz" title="Kontravalenz">Kontravalenz</a> <span class="mwe-math-element mwe-math-element-inline"><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{\dot {\vee }}Q}">

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<annotation encoding="application/x-tex">{\displaystyle P{\dot {\vee }}Q}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/70030798499bcb28b571f491cfb1f973194b8cdb.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.134ex; height:2.843ex;" alt="{\displaystyle P{\dot {\vee }}Q}" loading="lazy"></span> beziehungsweise <span class="mwe-math-element mwe-math-element-inline"><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\oplus Q}">

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<annotation encoding="application/x-tex">{\displaystyle P\oplus Q}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/704fb5f81fe3eba4d070096d7be4816190c6616f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.424ex; height:2.509ex;" alt="{\displaystyle P\oplus Q}" loading="lazy"></span>, auch Alternation oder ausschließendes Oder genannt: „entweder P oder Q, aber nicht beide“</li>

<li>das <a href="Bikonditional" title="Bikonditional">Bikonditional</a>, auch oder Äquivalenz genannt, <span class="mwe-math-element mwe-math-element-inline"><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\leftrightarrow Q}">

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<annotation encoding="application/x-tex">{\displaystyle P\leftrightarrow Q}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/43e9c3ed4d9717db81fc3794218f377bea4f6eb0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.198ex; height:2.509ex;" alt="{\displaystyle P\leftrightarrow Q}" loading="lazy"></span> beziehungsweise <span class="mwe-math-element mwe-math-element-inline"><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\Leftrightarrow Q}">

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<annotation encoding="application/x-tex">{\displaystyle P\Leftrightarrow Q}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/fe75af42226920bc628ac7bbd53c023928f346ba.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.198ex; height:2.509ex;" alt="{\displaystyle P\Leftrightarrow Q}" loading="lazy"></span>, entspricht einer hinreichenden und notwendigen Bedingung, „Q genau dann, wenn P“</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Extensionalität"><span id="Extensionalit.C3.A4t"></span>Extensionalität</h2></div>

<p>Man nennt einen Operator <i><a href="Wahrheitsfunktional" class="mw-redirect" title="Wahrheitsfunktional">wahrheitsfunktional</a></i> oder <i>extensional</i>, wenn der <a href="Wahrheitswert" title="Wahrheitswert">Wahrheitswert</a> eines durch ihn gebildeten zusammengesetzten Satzes eindeutig durch die Wahrheitswerte seiner Teilsätze bestimmt ist.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> Die Junktoren der <a href="Klassische_Logik" title="Klassische Logik">klassischen Aussagenlogik</a> sind in diesem Sinne extensional. Für eine genauere Definition von Extensionalität siehe <a href="Extensionalit%C3%A4tsprinzip" title="Extensionalitätsprinzip">Extensionalitätsprinzip</a>.

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<div class="mw-heading mw-heading3"><h3 id="Wahrheitstafeln">Wahrheitstafeln</h3></div>

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<caption>Schema: Wahrheitstafel für einen zweistelligen Junktor einer zweiwertigen Logik

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<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span></th>

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<annotation encoding="application/x-tex">{\displaystyle Q}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8752c7023b4b3286800fe3238271bbca681219ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" loading="lazy"></span></th>

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<annotation encoding="application/x-tex">{\displaystyle P\circ Q}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b6557e33da0703949ad06244925040ce32963f94.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.778ex; height:2.509ex;" alt="{\displaystyle P\circ Q}" loading="lazy"></span>

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<annotation encoding="application/x-tex">{\displaystyle WHW(P\circ Q)}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/df2dda3bafe935b388a7cfea5cd3cb8f4fc73610.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.522ex; height:2.843ex;" alt="{\displaystyle WHW(P\circ Q)}" loading="lazy"></span>,<br> für <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle WHW(P)=}">

</mstyle>

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<annotation encoding="application/x-tex">{\displaystyle WHW(P)=}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f63cbd1dc222d57502bbd4ea788712739181d26b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.942ex; height:2.843ex;" alt="{\displaystyle WHW(P)=}" loading="lazy"></span>w und <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle WHW(Q)=}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle WHW(Q)=}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e6186e68c1479a57ba808221f7c8ca23e0eed53a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.035ex; height:2.843ex;" alt="{\displaystyle WHW(Q)=}" loading="lazy"></span>w

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</mstyle>

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<annotation encoding="application/x-tex">{\displaystyle WHW(P\circ Q)}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/df2dda3bafe935b388a7cfea5cd3cb8f4fc73610.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.522ex; height:2.843ex;" alt="{\displaystyle WHW(P\circ Q)}" loading="lazy"></span>,<br> für <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle WHW(P)=}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle WHW(P)=}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f63cbd1dc222d57502bbd4ea788712739181d26b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.942ex; height:2.843ex;" alt="{\displaystyle WHW(P)=}" loading="lazy"></span>w und <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle WHW(Q)=}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle WHW(Q)=}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e6186e68c1479a57ba808221f7c8ca23e0eed53a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.035ex; height:2.843ex;" alt="{\displaystyle WHW(Q)=}" loading="lazy"></span>f

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</mstyle>

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<annotation encoding="application/x-tex">{\displaystyle WHW(P\circ Q)}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/df2dda3bafe935b388a7cfea5cd3cb8f4fc73610.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.522ex; height:2.843ex;" alt="{\displaystyle WHW(P\circ Q)}" loading="lazy"></span>,<br> für <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle WHW(P)=}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle WHW(P)=}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f63cbd1dc222d57502bbd4ea788712739181d26b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.942ex; height:2.843ex;" alt="{\displaystyle WHW(P)=}" loading="lazy"></span>f und <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle WHW(Q)=}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle WHW(Q)=}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e6186e68c1479a57ba808221f7c8ca23e0eed53a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.035ex; height:2.843ex;" alt="{\displaystyle WHW(Q)=}" loading="lazy"></span>w

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</mstyle>

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<annotation encoding="application/x-tex">{\displaystyle WHW(P\circ Q)}</annotation>

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</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/df2dda3bafe935b388a7cfea5cd3cb8f4fc73610.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.522ex; height:2.843ex;" alt="{\displaystyle WHW(P\circ Q)}" loading="lazy"></span>,<br> für <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle WHW(P)=}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle WHW(P)=}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f63cbd1dc222d57502bbd4ea788712739181d26b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.942ex; height:2.843ex;" alt="{\displaystyle WHW(P)=}" loading="lazy"></span>f und <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle WHW(Q)=}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle WHW(Q)=}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e6186e68c1479a57ba808221f7c8ca23e0eed53a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.035ex; height:2.843ex;" alt="{\displaystyle WHW(Q)=}" loading="lazy"></span>f

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<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span>“ und „<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8752c7023b4b3286800fe3238271bbca681219ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" loading="lazy"></span>“ sind zwei beliebige Aussagen, „<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \circ }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \circ }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/99add39d2b681e2de7ff62422c32704a05c7ec31.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.125ex; margin-bottom: -0.297ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle \circ }" loading="lazy"></span>“ steht für die Verknüpfung als logische Operation, „<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle WHW}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle WHW}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d71c0fab5e28d565ec5694162dbf25c04b010897.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.934ex; height:2.176ex;" alt="{\displaystyle WHW}" loading="lazy"></span>“ für Wahrheitswert, „w“ für den Wahrheitswert „Das Wahre“, „f“ für den Wahrheitswert „Das Falsche“.</small>

</td></tr></tbody></table>

<p>Eine Methode, den Wahrheitswertverlauf extensionaler Junktoren in einer Logik mit endlich vielen Wahrheitswerten übersichtlich darzustellen, sind die sogenannten <a href="Wahrheitstafel" class="mw-redirect" title="Wahrheitstafel">Wahrheitstafeln</a>. Bei diesen wird in jeder Zeile für eine mittels des Junktors aus Einzelaussagen gebildete zusammengesetzte Gesamtaussage für jede mögliche <i>Zuordnung</i> von Wahrheitswerten zu den Einzelaussagen der Wahrheitswert der Gesamtaussage angegeben. Für einen zweistelligen Junktor einer zweistelligen Logik könnte eine Wahrheitstafel wie in der Tabelle rechts aussehen:

</p>

<div class="mw-heading mw-heading3"><h3 id="Mögliche_Junktoren"><span id="M.C3.B6gliche_Junktoren"></span>Mögliche Junktoren</h3></div>

<p>Die Anzahl der Aussagen, die (beziehungsweise mit denen sich) ein Operator zu einer neuen Aussage verknüpft, nennt man seine <a href="Stelligkeit" title="Stelligkeit">Stelligkeit</a>: Ein einstelliger Operator verbindet sich mit einer einzigen Aussage zu einer neuen Aussage, zweistellige Junktoren verbinden sich mit zwei Aussagen zu einer neuen Aussage und so weiter. Allgemein verbindet ein n-stelliger Junktor sich mit n Aussagen zu einer neuen.

</p><p>Die Stelligkeit ist nicht zu verwechseln mit der Wertigkeit, d. h. mit der Frage, wie viele Wahrheitswerte zugelassen werden (vgl. <a href="Bivalenzprinzip" class="mw-redirect" title="Bivalenzprinzip">Bivalenzprinzip</a>).

</p><p>In der <a href="Klassische_Logik" title="Klassische Logik">klassischen Logik</a> ist der wichtigste einstellige Junktor die <a href="Negation" title="Negation">Negation</a>. Wichtige zweistellige Junktoren sind die Konjunktion und die <a href="Disjunktion" title="Disjunktion">Disjunktion</a> (oft werden nur diese beiden verwendet). Ebenso lassen sich klassische drei- und mehrstellige Junktoren auf Kombinationen ein- und zweistelliger Junktoren zurückführen.

</p><p>Allgemein gibt es für eine <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle m}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0a07d98bb302f3856cbabc47b2b9016692e3f7bc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}" loading="lazy"></span>-wertige Logik, d. h. für eine Logik mit endlich vielen Wahrheitswerten, deren Anzahl m ist, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m^{m^{n}}}">

<msup>

<msup>

</mrow>

</msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle m^{m^{n}}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6763a130b4ba0fe9cfc432d3ff3b07835206abdf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:4.68ex; height:2.676ex;" alt="{\displaystyle m^{m^{n}}}" loading="lazy"></span> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle n}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a601995d55609f2d9f5e233e36fbe9ea26011b3b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}" loading="lazy"></span>-stellige wahrheitsfunktionale Junktoren. Für die zweiwertige Aussagenlogik gibt es also <span class="mwe-math-element mwe-math-element-inline"><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^{1}}=4}">

<msup>

<msup>

</mrow>

</msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 2^{2^{1}}=4}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d438aa0b874b18decfa36c13b3d0b48a30cfc52c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.309ex; height:3.009ex;" alt="{\displaystyle 2^{2^{1}}=4}" loading="lazy"></span> einstellige Junktoren und <span class="mwe-math-element mwe-math-element-inline"><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^{2}}=16}">

<msup>

<msup>

</mrow>

</msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 2^{2^{2}}=16}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0a965faa7318db828f7d14d6dd5da15763b4871f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.472ex; height:3.009ex;" alt="{\displaystyle 2^{2^{2}}=16}" loading="lazy"></span> zweistellige Junktoren. Schon für die dreiwertige Aussagenlogik gibt es <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3^{3^{1}}=27}">

<msup>

<msup>

</mrow>

</msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 3^{3^{1}}=27}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a71948b51cb896f66ae66323aa742e70866e9b26.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.472ex; height:3.009ex;" alt="{\displaystyle 3^{3^{1}}=27}" loading="lazy"></span> einstellige und <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 3^{3^{2}}=19\,683}">

<msup>

<msup>

</mrow>

</msup>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle 3^{3^{2}}=19\,683}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/21a31177bdb76bc9ef1ab0efdea2ce4b21b24e2c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:12.346ex; height:3.009ex;" alt="{\displaystyle 3^{3^{2}}=19\,683}" loading="lazy"></span> zweistellige Junktoren.

</p><p>Die sechzehn zweistelligen Junktoren der zweiwertigen Logik sind in nachfolgender Tabelle dargestellt.

</p>

<caption>Tafel der zweistelligen Junktoren einer zweiwertigen Logik

</caption>

<th width="30%">Namen</th>

<th colspan="4" width="30%">Wahrheitswerte</th>

<th>Symbole</th>

<th>Formel

</th></tr>

<tr>

<td>

</td>

<td>

<table>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8752c7023b4b3286800fe3238271bbca681219ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" loading="lazy"></span>

</td></tr>

<tr>

<td style="border:none; padding:0px; border-collapse: collapse;">w

</td>

<td style="border:none; padding:0px; border-collapse: collapse;">w

</td></tr></tbody></table>

</td>

<td>

<table>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8752c7023b4b3286800fe3238271bbca681219ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" loading="lazy"></span>

</td></tr>

<tr>

<td style="border:none; padding:0px; border-collapse: collapse;">w

</td>

<td style="border:none; padding:0px; border-collapse: collapse;">f

</td></tr></tbody></table>

</td>

<td>

<table>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8752c7023b4b3286800fe3238271bbca681219ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" loading="lazy"></span>

</td></tr>

<tr>

<td style="border:none; padding:0px; border-collapse: collapse;">f

</td>

<td style="border:none; padding:0px; border-collapse: collapse;">w

</td></tr></tbody></table>

</td>

<td>

<table>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8752c7023b4b3286800fe3238271bbca681219ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" loading="lazy"></span>

</td></tr>

<tr>

<td style="border:none; padding:0px; border-collapse: collapse;">f

</td>

<td style="border:none; padding:0px; border-collapse: collapse;">f

</td></tr></tbody></table>

</td>

<td>

</td></tr>

<tr>

<td><a href="Kontradiktion" title="Kontradiktion">Kontradiktion</a></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \bot }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/f282c7bc331cc3bfcf1c57f1452cc23c022f58de.svg" 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 }" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P~\land ~\neg P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b9e46b7683c6746e106c771e7c374947a71f50cf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.785ex; height:2.176ex;" alt="{\displaystyle P~\land ~\neg P}" loading="lazy"></span>

</td></tr>

<tr>

<td><a href="Konjunktion_(Logik)" title="Konjunktion (Logik)">Konjunktion</a></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1caa4004cb216ef2930bb12fe805a76870caed94.svg" 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 }" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P~\land ~Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6bc76ce876240b07ad908ad3b2f2c34e7393da5d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.328ex; height:2.509ex;" alt="{\displaystyle P~\land ~Q}" loading="lazy"></span>

</td></tr>

<tr>

<td>Postsektion, Nur P</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \not \rightarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/cb95f3f5a9898c871045935a253d1d23e0e2644b.svg" 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 }" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><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 }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \not \supset }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0066ef658b08a8a21cf267a4e5bec61bc03fcb73.svg" 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 }" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P~\land ~\neg Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a8ab455ffc01e1504ba05b40f65b498e946dea55.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.878ex; height:2.509ex;" alt="{\displaystyle P~\land ~\neg Q}" loading="lazy"></span>

</td></tr>

<tr>

<td>Präpendenz, Identität von P</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \rfloor }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/9f94b873b2dd55ee745feec4b209feb7ccc531a8.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.032ex; height:2.843ex;" alt="{\displaystyle \rfloor }" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span>

</td></tr>

<tr>

<td>Präsektion, Nur Q</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \not \leftarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4acf12661d69611db01ff7f036bf8c5b5dfec902.svg" 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 }" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><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 }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \not \subset }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5b8e16e392d3856efb6355f906bf3d7b35f7f2ec.svg" 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 }" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle ~\neg P~\land ~Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/db1988fc6f7243b6c71b2d695b5472ba64aecc12.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.459ex; height:2.509ex;" alt="{\displaystyle ~\neg P~\land ~Q}" loading="lazy"></span>

</td></tr>

<tr>

<td>Postpendenz, <a href="Identit%C3%A4t" title="Identität">Identität</a> von Q</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \lfloor }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5d9b0450638f8cc086bb3f75f397bcc95edcd125.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.032ex; height:2.843ex;" alt="{\displaystyle \lfloor }" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8752c7023b4b3286800fe3238271bbca681219ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" loading="lazy"></span>

</td></tr>

<tr>

<td><a href="Kontravalenz" title="Kontravalenz">Kontravalenz</a>, ausschließende Disjunktion, <a href="XOR" class="mw-redirect" title="XOR">XOR</a></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \not \leftrightarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/363ed81fd02da85c658dde9f17737c13b7263e49.svg" 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 }" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><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 }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \not \equiv }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7d130bfc3eff6deb5c732a636f866cd9e373c197.svg" 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 }" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \veebar }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \veebar }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/04d326b0ae464569ba667f5b56e0541a4efe6bb4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.42ex; height:2.176ex;" alt="{\displaystyle \veebar }" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\dot {\vee }}}">

<mover>

</mover>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\dot {\vee }}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e489691ea7d6ac0c6598efef8525ed22d1b54c9c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.509ex;" alt="{\displaystyle {\dot {\vee }}}" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><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 }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \oplus }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8b16e2bdaefee9eed86d866e6eba3ac47c710f60.svg" 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 }" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \neg (P~\leftrightarrow ~Q)}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a28f51f2d18c9e50e061e7134f3f59ee65ce3651.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.719ex; height:2.843ex;" alt="{\displaystyle \neg (P~\leftrightarrow ~Q)}" loading="lazy"></span>

</td></tr>

<tr>

<td><a href="Disjunktion" title="Disjunktion">Disjunktion</a>, Adjunktion</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \vee }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7b76220c6805c9b465d6efbc7686c624f49f3023.svg" 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 }" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P~\lor ~Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/6f2e84c1358af547ce28214f46e41955ac306559.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.328ex; height:2.509ex;" alt="{\displaystyle P~\lor ~Q}" loading="lazy"></span>

</td></tr>

<tr>

<td><a href="Peirce-Funktion" class="mw-redirect" title="Peirce-Funktion">Peirce-Funktion</a>, NOR, Nihilition, Rejektion</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \downarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4618f22b0f780805eb94bb407578d9bc9487947a.svg" 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 }" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\overline {\vee }}}">

<mover>

</mover>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle {\overline {\vee }}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/a6f9bdf4cb18d1b79d370c396dc425e80f8340f7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.665ex; height:2.843ex;" alt="{\displaystyle {\overline {\vee }}}" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle ~\neg P~\land ~\neg Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2524131500bb913a97672a5c8eff6b0728ab422b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.009ex; height:2.509ex;" alt="{\displaystyle ~\neg P~\land ~\neg Q}" loading="lazy"></span>

</td></tr>

<tr>

<td><a href="Bikonditional" title="Bikonditional">Bikonditional</a>, <a href="Bijunktion" class="mw-redirect" title="Bijunktion">Bijunktion</a>, Äquivalenz</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \leftrightarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/046b918c43e05caf6624fe9b676c69ec9cd6b892.svg" 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 }" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \equiv }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \equiv }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4c5c34250859b6f6d2a77b4e8a2ceaa90638076d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.081ex; margin-bottom: -0.253ex; width:1.808ex; height:1.509ex;" alt="{\displaystyle \equiv }" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P~\leftrightarrow ~Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2446485465d252a1ed1e8c94aef0ce0d35a72b33.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.359ex; height:2.509ex;" alt="{\displaystyle P~\leftrightarrow ~Q}" loading="lazy"></span>

</td></tr>

<tr>

<td>Postnonpendenz, <a href="Negation" title="Negation">Negation</a> von Q</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \lceil }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0d4a554c972bf5a6fa5fca17e495479018227ebc.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.032ex; height:2.843ex;" alt="{\displaystyle \lceil }" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \neg Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/fad34798abb0bbbc063c906e459f103a09b1660e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.389ex; height:2.509ex;" alt="{\displaystyle \neg Q}" loading="lazy"></span>

</td></tr>

<tr>

<td><span id="Replikation_(Logik)"></span>Replikation</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \leftarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3c0fb4bce772117bbaf55b7ca1539ceff9ae218c.svg" 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 }" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><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 }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \subset }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/0f51f0eeff0c2a9dcb9c856f87ca0359e701ef01.svg" 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 }" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P~\leftarrow ~Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/d78ab33ef882c5478ce9f2e34b4f5a0119f25e45.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.359ex; height:2.509ex;" alt="{\displaystyle P~\leftarrow ~Q}" loading="lazy"></span>

</td></tr>

<tr>

<td>Pränonpendenz, <a href="Negation" title="Negation">Negation</a> von P</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \rceil }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8f59bbec141763531779850d312d8b1f629abe3b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.032ex; height:2.843ex;" alt="{\displaystyle \rceil }" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \neg P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5eb0d6c8752f8c7256d69c62e77dfe4c466dbe58.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.296ex; height:2.176ex;" alt="{\displaystyle \neg P}" loading="lazy"></span>

</td></tr>

<tr>

<td><a href="Subjunktion" title="Subjunktion">Subjunktion</a>, <a href="Implikation#Wahrheitsfunktionale_Implikation" title="Implikation">Implikation</a>, Konditional</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \rightarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/53e574cc3aa5b4bf5f3f5906caf121a378eef08b.svg" 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 }" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><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 }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \supset }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/27bfe0828a2ed4c9c6b70987a85c02a1f005843c.svg" 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 }" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P~\rightarrow ~Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c34701077d6bcfbb7262006a2a908822581901cf.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.359ex; height:2.509ex;" alt="{\displaystyle P~\rightarrow ~Q}" loading="lazy"></span>

</td></tr>

<tr>

<td><a href="Shefferscher_Strich" title="Shefferscher Strich">Sheffer-Funktion</a>, <a href="NAND-Gatter" title="NAND-Gatter">NAND</a>, Exklusion</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \mid }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8f7b2136e276c4aec285a6c40b91180c16432b9b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:0.647ex; height:2.843ex;" alt="{\displaystyle \mid }" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><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 }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \uparrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ddb20b28c74cdaa09e1f101d426441da1996072f.svg" 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 }" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \barwedge }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \barwedge }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/594efe4b2136418958bd9587ce8a583e93e024a4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.42ex; height:2.176ex;" alt="{\displaystyle \barwedge }" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle ~\neg P~\lor ~\neg Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/158f5e0955819936e1035a538ed32b9f1d36c919.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.009ex; height:2.509ex;" alt="{\displaystyle ~\neg P~\lor ~\neg Q}" loading="lazy"></span>

</td></tr>

<tr>

<td><a href="Tautologie_(Logik)" title="Tautologie (Logik)">Tautologie</a></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \top }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/cf12e436fef2365e76fcb1034a51179d8328bb33.svg" 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 }" loading="lazy"></span></td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P~\lor ~\neg P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/2b0dfddf2ae68e8a5d9f0e95aa0b9e853d00d80b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.785ex; height:2.176ex;" alt="{\displaystyle P~\lor ~\neg P}" loading="lazy"></span>

</td></tr></tbody></table>

<p>Um die enge Verbindung von Aussagenlogik und <a href="Mengenlehre" title="Mengenlehre">Mengenlehre</a> zu betonen, können Wahrheitstafeln auch <a href="Mengendiagramm#Euler-Diagramme" title="Mengendiagramm">Eulerdiagramm</a>-ähnlich dargestellt werden (siehe folgende Beispiele).

</p>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1caa4004cb216ef2930bb12fe805a76870caed94.svg" 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 }" loading="lazy"></span>

</td>

</td>

<td style="text-align:right; padding-left:0.5em;">w

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1caa4004cb216ef2930bb12fe805a76870caed94.svg" 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 }" loading="lazy"></span>

</td>

<td>f

</td></tr>

<tr>

<td style="text-align:right;">f

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1caa4004cb216ef2930bb12fe805a76870caed94.svg" 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 }" loading="lazy"></span>

</td>

<td>w

</td>

<td style="text-align:right;">f

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/1caa4004cb216ef2930bb12fe805a76870caed94.svg" 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 }" loading="lazy"></span>

</td>

<td>f

</td></tr>

<tr>

<td colspan="6" style="text-align:center;">Konjunktion

</td></tr></tbody></table></dd></dl>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \vee }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7b76220c6805c9b465d6efbc7686c624f49f3023.svg" 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 }" loading="lazy"></span>

</td>

</td>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \vee }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7b76220c6805c9b465d6efbc7686c624f49f3023.svg" 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 }" loading="lazy"></span>

</td>

</td></tr>

<tr>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \vee }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7b76220c6805c9b465d6efbc7686c624f49f3023.svg" 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 }" loading="lazy"></span>

</td>

</td>

<td style="text-align:right;">f

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \vee }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7b76220c6805c9b465d6efbc7686c624f49f3023.svg" 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 }" loading="lazy"></span>

</td>

<td>f

</td></tr>

<tr>

<td colspan="6" style="text-align:center;">Disjunktion

</td></tr></tbody></table>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \rightarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/53e574cc3aa5b4bf5f3f5906caf121a378eef08b.svg" 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 }" loading="lazy"></span>

</td>

</td>

<td style="text-align:right; padding-left:0.5em;">w

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \rightarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/53e574cc3aa5b4bf5f3f5906caf121a378eef08b.svg" 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 }" loading="lazy"></span>

</td>

<td>f

</td></tr>

<tr>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \rightarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/53e574cc3aa5b4bf5f3f5906caf121a378eef08b.svg" 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 }" loading="lazy"></span>

</td>

</td>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \rightarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/53e574cc3aa5b4bf5f3f5906caf121a378eef08b.svg" 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 }" loading="lazy"></span>

</td>

</td></tr>

<tr>

<td colspan="6" style="text-align:center;">Subjunktion

</td></tr></tbody></table>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \leftrightarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/046b918c43e05caf6624fe9b676c69ec9cd6b892.svg" 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 }" loading="lazy"></span>

</td>

</td>

<td style="text-align:right; padding-left:0.5em;">w

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \leftrightarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/046b918c43e05caf6624fe9b676c69ec9cd6b892.svg" 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 }" loading="lazy"></span>

</td>

<td>f

</td></tr>

<tr>

<td style="text-align:right;">f

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \leftrightarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/046b918c43e05caf6624fe9b676c69ec9cd6b892.svg" 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 }" loading="lazy"></span>

</td>

<td>w

</td>

</td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \leftrightarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/046b918c43e05caf6624fe9b676c69ec9cd6b892.svg" 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 }" loading="lazy"></span>

</td>

</td></tr>

<tr>

<td colspan="6" style="text-align:center;">Bikonditional

</td></tr></tbody></table>

<p>Die Terme in Fettschrift sind wahr, die in Normalschrift falsch.

</p>

<div class="mw-heading mw-heading3"><h3 id="Reduzierbarkeit_und_funktionale_Vollständigkeit"><span id="Reduzierbarkeit_und_funktionale_Vollst.C3.A4ndigkeit"></span>Reduzierbarkeit und funktionale Vollständigkeit</h3></div>

<p>Es ist möglich, einzelne Verknüpfungen durch andere auszudrücken; zum Beispiel lässt sich die Konjunktion <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A\land B}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle A\land B}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/74954195333a8593163b93a9688695b8dc74da55.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.09ex; height:2.176ex;" alt="{\displaystyle A\land B}" loading="lazy"></span> durch Disjunktion und Negation als <span class="mwe-math-element mwe-math-element-inline"><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 (\neg A\lor \neg B)}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \neg (\neg A\lor \neg B)}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/fdffb25cda99ba7533af46896d8471612e831b53.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.55ex; height:2.843ex;" alt="{\displaystyle \neg (\neg A\lor \neg B)}" loading="lazy"></span> oder <a href="Implikation" title="Implikation">Konditional</a> <span class="mwe-math-element mwe-math-element-inline"><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}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P\rightarrow Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/86439ea857adc8eaec93c4d14270b8ba6bd2a6a9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.198ex; height:2.509ex;" alt="{\displaystyle P\rightarrow Q}" loading="lazy"></span> durch die <a href="Disjunktion" title="Disjunktion">Disjunktion</a> <span class="mwe-math-element mwe-math-element-inline"><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 P\vee Q}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \neg P\vee Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/3dee89c718438f069ff81a0425b2ee722bbb2861.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.717ex; height:2.509ex;" alt="{\displaystyle \neg P\vee Q}" loading="lazy"></span> ausdrücken. Allgemein heißt eine Menge von Junktoren bezogen auf ein logisches System <i>funktional vollständig</i> oder <i>semantisch vollständig</i>, wenn mit Hilfe der betroffenen Konnektive alle anderen Konnektive des logischen Systems ausgedrückt werden können. Für die klassische Aussagenlogik sind zum Beispiel die Junktorenmengen <span class="mwe-math-element mwe-math-element-inline"><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 },{\land }\}}">

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \{{\neg },{\land }\}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/69ba20f58de3f212a0c73302eeeebae91fe54923.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.46ex; height:2.843ex;" alt="{\displaystyle \{{\neg },{\land }\}}" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><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 },{\lor }\}}">

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \{{\neg },{\lor }\}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/309452c576d688f34d5f101e7a4a3a8cefdd0d2b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.46ex; height:2.843ex;" alt="{\displaystyle \{{\neg },{\lor }\}}" loading="lazy"></span> und <span class="mwe-math-element mwe-math-element-inline"><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 },{\rightarrow }\}}">

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \{{\neg },{\rightarrow }\}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c3e05d4fcc3e24b3c8f28d1ee2bc3867768ac5fe.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.233ex; height:2.843ex;" alt="{\displaystyle \{{\neg },{\rightarrow }\}}" loading="lazy"></span> funktional vollständig. Das bedeutet, dass sich alle Junktoren der klassischen Aussagenlogik wahlweise auf Negation und Konjunktion, auf Negation und Disjunktion oder auf Negation und Konditional zurückführen lassen. Häufig verwendete Junktorenmengen sind <span class="mwe-math-element mwe-math-element-inline"><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 },{\land },{\lor }\}}">

</mrow>

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \{{\neg },{\land },{\lor }\}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/5f273472dda2603f4a65b98298d257d4dd306b0b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.044ex; height:2.843ex;" alt="{\displaystyle \{{\neg },{\land },{\lor }\}}" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><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 },{\land }\}}">

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \{{\neg },{\land }\}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/69ba20f58de3f212a0c73302eeeebae91fe54923.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.46ex; height:2.843ex;" alt="{\displaystyle \{{\neg },{\land }\}}" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><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 },{\lor }\}}">

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \{{\neg },{\lor }\}}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/309452c576d688f34d5f101e7a4a3a8cefdd0d2b.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.46ex; height:2.843ex;" alt="{\displaystyle \{{\neg },{\lor }\}}" loading="lazy"></span>.

</p><p>Tatsächlich ist es möglich, alle Verknüpfungen allein mit Hilfe <i>einer einzigen</i> Verknüpfung darzustellen, und zwar mit der Shefferfunktion (NAND), aber auch mit der Peirce-Funktion (NOR).

</p>

<div class="mw-heading mw-heading3"><h3 id="Sheffer-Operatoren">Sheffer-Operatoren</h3></div>

<p>Wenn sich mit einem Junktor allein, d. h. ganz ohne Hinzunahme weiterer Junktoren alle anderen Junktoren ausdrücken lassen, dann wird dieser Junktor <i>Sheffer-Operator</i> oder <i>Shefferfunktion</i> (nach <a href="Henry_Maurice_Sheffer" title="Henry Maurice Sheffer">Henry Maurice Sheffer</a>) genannt. Für die klassische Aussagenlogik gibt es genau zwei Sheffer-Operatoren: den <a href="Shefferscher_Strich" title="Shefferscher Strich">Shefferstrich</a>, auch NAND genannt (<span class="mwe-math-element mwe-math-element-inline"><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 }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \uparrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/ddb20b28c74cdaa09e1f101d426441da1996072f.svg" 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 }" loading="lazy"></span> oder <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \vert }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \vert }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/93019cea46f1a0aaef5215a0bba66cb0078942d9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:0.647ex; height:2.843ex;" alt="{\displaystyle \vert }" loading="lazy"></span>) und den <a href="Peirce-Funktion" class="mw-redirect" title="Peirce-Funktion">Peirce-Operator</a>, auch NOR genannt <span class="mwe-math-element mwe-math-element-inline"><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 }">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \downarrow }</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4618f22b0f780805eb94bb407578d9bc9487947a.svg" 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 }" loading="lazy"></span>.

</p>

<div class="mw-heading mw-heading2"><h2 id="Intensionale_Operatoren">Intensionale Operatoren</h2></div>

<p>Logische Operatoren, bei denen der Wahrheitswert eines aus ihnen gebildeten Satzes nicht eindeutig von den Wahrheitswerten ihrer Teilsätze bestimmt ist, heißen <i>intensionale Junktoren</i>. Intensional sind z. B. die einstelligen Modaloperatoren „es ist notwendig, dass“ und „es ist möglich, dass“ (siehe <a href="Modallogik" title="Modallogik">Modallogik</a>): Dass eine Aussage wahr ist, bedeutet noch nicht, dass diese Aussage auch notwendig ist. Dass eine Aussage falsch ist, bedeutet noch nicht, dass sie unmöglich ist. Wahrheitsfunktional lässt sich den Modalitäten daher wohl nicht beikommen.

</p><p>Zur Interpretation intensionaler Junktoren benötigt man komplexere Modelle als die extensionalen Wahrheitstabellen. Die erste bedeutende <a href="Formale_Semantik" title="Formale Semantik">formale Semantik</a> intensionaler Junktoren ist wohl die von <a href="Saul_Kripke" title="Saul Kripke">Saul Kripke</a> ursprünglich zur Interpretation der Modallogik entwickelte Kripke-Semantik (siehe <a href="Modallogik" title="Modallogik">Modallogik</a>). Kripke-Semantik eignet sich auch zur Interpretation intuitionistischer Logik.

</p>

<div class="sieheauch" role="navigation" style="font-style:italic;"><span class="sieheauch-text">Siehe auch</span>: <a href="Logik#Philosophische_Logiken" title="Logik">Philosophische Logik</a></div>

<div class="mw-heading mw-heading2"><h2 id="Beispiele">Beispiele</h2></div>

<th width="25%">Wahrheitstafel für die Konjunktion <br> in der zweiwertigen klassischen Logik

</th>

<th width="25%">Wahrheitstafel für die <a href="Disjunktion" title="Disjunktion">Disjunktion</a> <br> in der zweiwertigen klassischen Logik

</th>

<th width="25%">Wahrheitstafel für die materiale <a href="Implikation" title="Implikation">Implikation</a> <br> in der zweiwertigen klassischen Logik

</th>

<th width="25%">Wahrheitstafel für den Konjunktor <br> in der dreiwertigen Logik Ł3 <br> von <a href="Jan_%C5%81ukasiewicz" title="Jan Łukasiewicz">Jan Łukasiewicz</a> (1920)

</th></tr>

<tr>

<td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span></th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8752c7023b4b3286800fe3238271bbca681219ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" loading="lazy"></span></th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P\land Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c5690bb4822d8c821a00cfe3c6644b046a884af4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.166ex; height:2.509ex;" alt="{\displaystyle P\land Q}" loading="lazy"></span>

</th></tr>

<tr>

<td>wahr

</td></tr>

<tr>

<td>falsch</td>

<td>falsch

</td></tr>

<tr>

<td>falsch</td>

<td>falsch

</td></tr>

<tr>

<td>falsch</td>

<td>falsch

</td></tr></tbody></table>

</td>

<td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span></th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8752c7023b4b3286800fe3238271bbca681219ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" loading="lazy"></span></th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P\lor Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/7d2bc60d4b9ff5ec772fec5c2ef72a39536d4323.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.166ex; height:2.509ex;" alt="{\displaystyle P\lor Q}" loading="lazy"></span>

</th></tr>

<tr>

<td>wahr

</td></tr>

<tr>

<td>falsch</td>

<td>wahr

</td></tr>

<tr>

<td>falsch</td>

<td>wahr

</td></tr>

<tr>

<td>falsch</td>

<td>falsch

</td></tr></tbody></table>

</td>

<td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span></th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8752c7023b4b3286800fe3238271bbca681219ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" loading="lazy"></span></th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P\rightarrow Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/86439ea857adc8eaec93c4d14270b8ba6bd2a6a9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.198ex; height:2.509ex;" alt="{\displaystyle P\rightarrow Q}" loading="lazy"></span>

</th></tr>

<tr>

<td>wahr

</td></tr>

<tr>

<td>falsch</td>

<td>falsch

</td></tr>

<tr>

<td>falsch</td>

<td>wahr

</td></tr>

<tr>

<td>falsch</td>

<td>wahr

</td></tr></tbody></table>

</td>

<td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span></th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8752c7023b4b3286800fe3238271bbca681219ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" loading="lazy"></span></th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P\land Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c5690bb4822d8c821a00cfe3c6644b046a884af4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.166ex; height:2.509ex;" alt="{\displaystyle P\land Q}" loading="lazy"></span>

</th></tr>

<tr>

<td>1

</td></tr>

<tr>

<td>½

</td></tr>

<tr>

<td>0

</td></tr>

<tr>

<td>½

</td></tr>

<tr>

<td>½

</td></tr>

<tr>

<td>0

</td></tr>

<tr>

<td>0

</td></tr>

<tr>

<td>0

</td></tr>

<tr>

<td>0

</td></tr></tbody></table>

</td></tr>

<th width="20%">Wahrheitstafel für den Konjunktor <br> in der dreiwertigen Logik B3 <br> von Dimitri Anatoljewitsch Bočvar (1938)

</th>

<th colspan="3">In der <a href="Dialogische_Logik" title="Dialogische Logik">Dialogischen Logik</a>

</th></tr>

<tr>

<td>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span></th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8752c7023b4b3286800fe3238271bbca681219ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" loading="lazy"></span></th>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P\land Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/c5690bb4822d8c821a00cfe3c6644b046a884af4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.166ex; height:2.509ex;" alt="{\displaystyle P\land Q}" loading="lazy"></span>

</th></tr>

<tr>

<td>1

</td></tr>

<tr>

<td>½

</td></tr>

<tr>

<td>0

</td></tr>

<tr>

<td>½

</td></tr>

<tr>

<td>½

</td></tr>

<tr>

<td>½

</td></tr>

<tr>

<td>0

</td></tr>

<tr>

<td>½

</td></tr>

<tr>

<td>0

</td></tr></tbody></table>

</td>

<th width="20%">Opponent</th>

<th width="20%">Proponent</th>

<th>

</th></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P\rightarrow Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/86439ea857adc8eaec93c4d14270b8ba6bd2a6a9.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.198ex; height:2.509ex;" alt="{\displaystyle P\rightarrow Q}" loading="lazy"></span>

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P?}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/83e6dca37c24b671ea065d03c0ee4d5fdfa3fcda.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.843ex; height:2.176ex;" alt="{\displaystyle P?}" loading="lazy"></span></td>

<td>Die Subjunktionsbehauptung wird angegriffen nach der Subjunktionsregel: Die voranstehende <span class="mwe-math-element mwe-math-element-inline"><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}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span> wird behauptet.

</td></tr>

<tr>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8752c7023b4b3286800fe3238271bbca681219ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" loading="lazy"></span></td>

<td>Als Verteidigung wird das nachstehende <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Q}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle Q}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/8752c7023b4b3286800fe3238271bbca681219ed.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.838ex; height:2.509ex;" alt="{\displaystyle Q}" loading="lazy"></span> genannt, dies kann durch eine Übernahme des <span class="mwe-math-element mwe-math-element-inline"><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}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span> der vorigen Zeile verteidigt werden. Es kann – je nach Regelsatz – auch erst die Aussage <span class="mwe-math-element mwe-math-element-inline"><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}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle P}</annotation>

</semantics>

</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/b4dc73bf40314945ff376bd363916a738548d40a.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}" loading="lazy"></span> angegriffen werden.

</td></tr></tbody></table>

<div class="mw-heading mw-heading2"><h2 id="Literatur">Literatur</h2></div>

<ul><li><a href="Benjamin_Schnieder" title="Benjamin Schnieder">Benjamin Schnieder</a>: <i>Junktoren</i>, in: Nikola Kompa (Hrsg.): <i>Handbuch Sprachphilosophie</i>. Metzler, Stuttgart 2015, ISBN 978-3-476-02509-8, S. 166–173.</li></ul>

<div class="mw-heading mw-heading2"><h2 id="Weblinks">Weblinks</h2></div>

<div class="sisterproject" style="margin:0.1em 0 0 0;"><div class="noviewer" style="display:inline-block; line-height:10px; min-width:1.6em; text-align:center;" aria-hidden="true" role="presentation"><span class="mw-default-size" typeof="mw:File"><span title="Wikibooks"></span></span></div><b><a href="https://de.wikibooks.org/wiki/Mathe_f%C3%BCr_Nicht-Freaks:_Junktor" class="extiw external" title="b:Mathe für Nicht-Freaks: Junktor">Wikibooks: Mathe für Nicht-Freaks: Junktor</a></b> – Lern- und Lehrmaterialien</div>

<div class="sisterproject" style="margin:0.1em 0 0 0;"><span class="noviewer" style="display:inline-block; line-height:10px; min-width:1.6em; text-align:center;" aria-hidden="true" role="presentation"><span class="mw-default-size" typeof="mw:File"><span title="Wiktionary"></span></span></span><b><a href="https://de.wiktionary.org/wiki/Junktor" class="extiw external" title="wikt:Junktor">Wiktionary: Junktor</a></b> – Bedeutungserklärungen, Wortherkunft, Synonyme, Übersetzungen</div>

<div class="mw-heading mw-heading2"><h2 id="Einzelnachweise">Einzelnachweise</h2></div>

<li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Matthias Hieber: <cite style="font-style:italic">Analysis I</cite>. 1. Auflage. Springer Spektrum, Berlin 2018, ISBN 978-3-662-57537-6, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>3</span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Junktor&rft.au=Matthias+Hieber&rft.btitle=Analysis+I&rft.date=2018&rft.edition=1&rft.genre=book&rft.isbn=9783662575376&rft.pages=3&rft.place=Berlin&rft.pub=Springer+Spektrum" style="display:none"> </span></span>

</li>

<li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Gerhard Schurz: <cite style="font-style:italic">Logik: Grund- und Aufbaukurs in Aussagen- und Prädikatenlogik</cite>. 2. Auflage. Walter de Gruyter, Berlin / Boston 2020, ISBN 978-3-11-069714-8, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>33</span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Junktor&rft.au=Gerhard+Schurz&rft.btitle=Logik%3A+Grund-+und+Aufbaukurs+in+Aussagen-+und+Pr%C3%A4dikatenlogik&rft.date=2020&rft.edition=2&rft.genre=book&rft.isbn=9783110697148&rft.pages=33&rft.place=Berlin+%2F+Boston&rft.pub=Walter+de+Gruyter" style="display:none"> </span></span>

</li>

<li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Gerhard Schurz: <cite style="font-style:italic">Logik: Grund- und Aufbaukurs in Aussagen-

und Prädikatenlogik</cite>. 2. Auflage. Walter de Gruyter, Berlin / Boston 2020, ISBN 978-3-11-069714-8, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>13</span>.<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Junktor&rft.au=Gerhard+Schurz&rft.btitle=Logik%3A+Grund-+und+Aufbaukurs+in+Aussagen-%0Aund+Pr%C3%A4dikatenlogik&rft.date=2020&rft.edition=2&rft.genre=book&rft.isbn=9783110697148&rft.pages=13&rft.place=Berlin+%2F+Boston&rft.pub=Walter+de+Gruyter" style="display:none"> </span></span>

</li>

</ol></dd></dl></div><div><div class="zim-footer">

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