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class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9A%D0%BB%D1%8F%D1%81%D1%8B%D1%87%D0%BD%D0%B0%D1%8F_%D0%BB%D1%91%D0%B3%D1%96%D0%BA%D0%B0" title="Клясычная лёгіка – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Клясычная лёгіка" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/L%C3%B2gica_cl%C3%A0ssica" title="Lògica clàssica – Catalan" lang="ca" hreflang="ca" data-title="Lògica clàssica" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Klassische_Logik" title="Klassische Logik – German" lang="de" hreflang="de" data-title="Klassische Logik" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Klassikaline_loogika" title="Klassikaline loogika – Estonian" lang="et" hreflang="et" data-title="Klassikaline loogika" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/L%C3%B3gica_cl%C3%A1sica" title="Lógica clásica – Spanish" lang="es" hreflang="es" data-title="Lógica clásica" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Klasika_logiko" title="Klasika logiko – Esperanto" lang="eo" hreflang="eo" data-title="Klasika logiko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D9%86%D8%B7%D9%82_%DA%A9%D9%84%D8%A7%D8%B3%DB%8C%DA%A9" title="منطق کلاسیک – Persian" lang="fa" hreflang="fa" data-title="منطق کلاسیک" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Logique_classique" title="Logique classique – French" lang="fr" hreflang="fr" data-title="Logique classique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/L%C3%B3xica_cl%C3%A1sica" title="Lóxica clásica – Galician" lang="gl" hreflang="gl" data-title="Lóxica clásica" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B3%A0%EC%A0%84_%EB%85%BC%EB%A6%AC" title="고전 논리 – Korean" lang="ko" hreflang="ko" data-title="고전 논리" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B6%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A5%80%E0%A4%AF_%E0%A4%A4%E0%A4%B0%E0%A5%8D%E0%A4%95%E0%A4%B6%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B0" title="शास्त्रीय तर्कशास्त्र – Hindi" lang="hi" hreflang="hi" data-title="शास्त्रीय तर्कशास्त्र" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Logica_classica" title="Logica classica – Italian" lang="it" hreflang="it" data-title="Logica classica" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9A%D0%BB%D0%B0%D1%81%D0%B8%D1%87%D0%BD%D0%B0_%D0%BB%D0%BE%D0%B3%D0%B8%D0%BA%D0%B0" title="Класична логика – Macedonian" lang="mk" hreflang="mk" data-title="Класична логика" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Klassieke_logica" title="Klassieke logica – Dutch" lang="nl" hreflang="nl" data-title="Klassieke logica" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%8F%A4%E5%85%B8%E8%AB%96%E7%90%86" title="古典論理 – Japanese" lang="ja" hreflang="ja" data-title="古典論理" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/L%C3%B3gica_cl%C3%A1ssica" title="Lógica clássica – Portuguese" lang="pt" hreflang="pt" data-title="Lógica clássica" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a 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<div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Class of formal logics</div> <p><b>Classical logic</b> (or <b>standard logic</b>)<sup id="cite_ref-BunninYu2004_1-0" class="reference"><a href="#cite_note-BunninYu2004-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Gamut1991_2-0" class="reference"><a href="#cite_note-Gamut1991-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> or <b>Frege–Russell logic</b><sup id="cite_ref-Kanamori2000_3-0" class="reference"><a href="#cite_note-Kanamori2000-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> is the intensively studied and most widely used class of <a href="/wiki/Deductive_logic" class="mw-redirect" title="Deductive logic">deductive logic</a>.<sup id="cite_ref-:0_4-0" class="reference"><a href="#cite_note-:0-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> Classical logic has had much influence on <a href="/wiki/Analytic_philosophy" title="Analytic philosophy">analytic philosophy</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Characteristics">Characteristics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Classical_logic&action=edit&section=1" title="Edit section: Characteristics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Each logical system in this class shares characteristic properties:<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <ol><li><a href="/wiki/Law_of_excluded_middle" title="Law of excluded middle">Law of excluded middle</a> and <a href="/wiki/Double_negation_elimination" class="mw-redirect" title="Double negation elimination">double negation elimination</a></li> <li><a href="/wiki/Law_of_noncontradiction" title="Law of noncontradiction">Law of noncontradiction</a>, and the <a href="/wiki/Principle_of_explosion" title="Principle of explosion">principle of explosion</a></li> <li><a href="/wiki/Monotonicity_of_entailment" title="Monotonicity of entailment">Monotonicity of entailment</a> and <a href="/wiki/Idempotency_of_entailment" class="mw-redirect" title="Idempotency of entailment">idempotency of entailment</a></li> <li><a href="/wiki/Commutativity_of_conjunction" title="Commutativity of conjunction">Commutativity of conjunction</a></li> <li><a href="/wiki/De_Morgan_duality" class="mw-redirect" title="De Morgan duality">De Morgan duality</a>: every <a href="/wiki/Logical_operator" class="mw-redirect" title="Logical operator">logical operator</a> is dual to another</li></ol> <p>While not entailed by the preceding conditions, contemporary discussions of classical logic normally only include <a href="/wiki/Propositional_calculus" title="Propositional calculus">propositional</a> and <a href="/wiki/First-order_logic" title="First-order logic">first-order</a> logics.<sup id="cite_ref-:0_4-1" class="reference"><a href="#cite_note-:0-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-haack_6-0" class="reference"><a href="#cite_note-haack-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> In other words, the overwhelming majority of time spent studying classical logic has been spent studying specifically propositional and first-order logic, as opposed to the other forms of classical logic. </p><p>Most semantics of classical logic are <a href="/wiki/Principle_of_bivalence" title="Principle of bivalence">bivalent</a>, meaning all of the possible denotations of propositions can be categorized as either true or false. </p> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Classical_logic&action=edit&section=2" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/History_of_logic" title="History of logic">History of logic</a></div> <p>Classical logic is a 19th and 20th-century innovation. The name does not refer to <a href="/wiki/Classical_antiquity" title="Classical antiquity">classical antiquity</a>, which used the <a href="/wiki/Term_logic" title="Term logic">term logic</a> of <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a>. Classical logic was the reconciliation of Aristotle's logic, which dominated most of the last 2000 years, with the propositional <a href="/wiki/Stoic_logic" title="Stoic logic">Stoic logic</a>. The two were sometimes seen as irreconcilable. </p><p><a href="/wiki/Leibniz" class="mw-redirect" title="Leibniz">Leibniz</a>'s <a href="/wiki/Calculus_ratiocinator" title="Calculus ratiocinator">calculus ratiocinator</a> can be seen as foreshadowing classical logic. <a href="/wiki/Bernard_Bolzano" title="Bernard Bolzano">Bernard Bolzano</a> has the understanding of <a href="/wiki/Existential_import" class="mw-redirect" title="Existential import">existential import</a> found in classical logic and not in Aristotle. Though he never questioned Aristotle, <a href="/wiki/George_Boole" title="George Boole">George Boole</a>'s algebraic reformulation of logic, so-called <a href="/wiki/Boolean_logic" class="mw-redirect" title="Boolean logic">Boolean logic</a>, was a predecessor of modern <a href="/wiki/Mathematical_logic" title="Mathematical logic">mathematical logic</a> and classical logic. <a href="/wiki/William_Stanley_Jevons" title="William Stanley Jevons">William Stanley Jevons</a> and <a href="/wiki/John_Venn" title="John Venn">John Venn</a>, who also had the modern understanding of existential import, expanded Boole's system. </p> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Begriffsschrift_Titel.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Begriffsschrift_Titel.png/250px-Begriffsschrift_Titel.png" decoding="async" width="180" height="282" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Begriffsschrift_Titel.png/330px-Begriffsschrift_Titel.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0c/Begriffsschrift_Titel.png/360px-Begriffsschrift_Titel.png 2x" data-file-width="361" data-file-height="566" /></a><figcaption>Begriffsschrift title page</figcaption></figure> <p>The original <a href="/wiki/First-order_logic" title="First-order logic">first-order</a>, classical logic is found in <a href="/wiki/Gottlob_Frege" title="Gottlob Frege">Gottlob Frege</a>'s <i><a href="/wiki/Begriffsschrift" title="Begriffsschrift">Begriffsschrift</a></i>. It has a wider application than Aristotle's logic and is capable of expressing Aristotle's logic as a special case. It explains the <a href="/wiki/Quantifier_(logic)" title="Quantifier (logic)">quantifiers</a> in terms of mathematical functions. It was also the first logic capable of dealing with the <a href="/wiki/Problem_of_multiple_generality" title="Problem of multiple generality">problem of multiple generality</a>, for which Aristotle's system was impotent. Frege, who is considered the founder of analytic philosophy, invented it to show all of mathematics was derivable from logic, and make <a href="/wiki/Arithmetic" title="Arithmetic">arithmetic</a> rigorous as <a href="/wiki/David_Hilbert" title="David Hilbert">David Hilbert</a> had done for <a href="/wiki/Geometry" title="Geometry">geometry</a>, the doctrine is known as <a href="/wiki/Logicism" title="Logicism">logicism</a> in the <a href="/wiki/Foundations_of_mathematics" title="Foundations of mathematics">foundations of mathematics</a>. The notation Frege used never much caught on. <a href="/wiki/Hugh_MacColl" title="Hugh MacColl">Hugh MacColl</a> published a variant of propositional logic two years prior. </p><p>The writings of <a href="/wiki/Augustus_De_Morgan" title="Augustus De Morgan">Augustus De Morgan</a> and <a href="/wiki/Charles_Sanders_Peirce" title="Charles Sanders Peirce">Charles Sanders Peirce</a> also pioneered classical logic with the logic of relations. Peirce influenced <a href="/wiki/Giuseppe_Peano" title="Giuseppe Peano">Giuseppe Peano</a> and <a href="/wiki/Ernst_Schr%C3%B6der_(mathematician)" title="Ernst Schröder (mathematician)">Ernst Schröder</a>. </p><p>Classical logic reached fruition in <a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a> and <a href="/wiki/A._N._Whitehead" class="mw-redirect" title="A. N. Whitehead">A. N. Whitehead</a>'s <i>Principia Mathematica</i>, and <a href="/wiki/Ludwig_Wittgenstein" title="Ludwig Wittgenstein">Ludwig Wittgenstein</a>'s <i><a href="/wiki/Tractatus_Logico_Philosophicus" class="mw-redirect" title="Tractatus Logico Philosophicus">Tractatus Logico Philosophicus</a></i>. Russell and Whitehead were influenced by Peano (it uses his notation) and Frege and sought to show mathematics was derived from logic. Wittgenstein was influenced by Frege and Russell and initially considered the <i>Tractatus</i> to have solved all problems of philosophy. </p><p><a href="/wiki/Willard_Van_Orman_Quine" title="Willard Van Orman Quine">Willard Van Orman Quine</a> believed that a formal system that allows quantification over predicates (<a href="/wiki/Higher-order_logic" title="Higher-order logic">higher-order logic</a>) didn't meet the requirements to be a logic, saying that it was "<a href="/wiki/Set_theory" title="Set theory">set theory</a> in disguise". </p><p>Classical logic is the standard logic of mathematics. Many mathematical theorems rely on classical rules of inference such as <a href="/wiki/Disjunctive_syllogism" title="Disjunctive syllogism">disjunctive syllogism</a> and the <a href="/wiki/Double_negation_elimination" class="mw-redirect" title="Double negation elimination">double negation elimination</a>. The adjective "classical" in logic is not related to the use of the adjective "classical" in physics, which has another meaning. In logic, "classical" simply means "standard". Classical logic should also not be confused with <a href="/wiki/Term_logic" title="Term logic">term logic</a>, also known as Aristotelian logic. </p><p><a href="/wiki/Jan_%C5%81ukasiewicz" title="Jan Łukasiewicz">Jan Łukasiewicz</a> pioneered <a href="/wiki/Non-classical_logic" title="Non-classical logic">non-classical logic</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Generalized_semantics">Generalized semantics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Classical_logic&action=edit&section=3" title="Edit section: Generalized semantics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>With the advent of <a href="/wiki/Algebraic_logic" title="Algebraic logic">algebraic logic</a>, it became apparent that classical <a href="/wiki/Propositional_calculus" title="Propositional calculus">propositional calculus</a> admits other <a href="/wiki/Semantics" title="Semantics">semantics</a>. In <a href="/wiki/Boolean-valued_semantics" class="mw-redirect" title="Boolean-valued semantics">Boolean-valued semantics</a> (for classical <a href="/wiki/Propositional_logic" class="mw-redirect" title="Propositional logic">propositional logic</a>), the truth values are the elements of an arbitrary <a href="/wiki/Boolean_algebra_(structure)" title="Boolean algebra (structure)">Boolean algebra</a>; "true" corresponds to the maximal element of the algebra, and "false" corresponds to the minimal element. Intermediate elements of the algebra correspond to truth values other than "true" and "false". The principle of bivalence holds only when the Boolean algebra is taken to be the <a href="/wiki/Two-element_Boolean_algebra" title="Two-element Boolean algebra">two-element algebra</a>, which has no intermediate elements. </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Classical_logic&action=edit&section=4" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-BunninYu2004-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-BunninYu2004_1-0">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFNicholas_BunninJiyuan_Yu2004" class="citation book cs1">Nicholas Bunnin; Jiyuan Yu (2004). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=OskKWI1YA7AC&pg=PA266"><i>The Blackwell dictionary of Western philosophy</i></a>. Wiley-Blackwell. p. 266. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4051-0679-5" title="Special:BookSources/978-1-4051-0679-5"><bdi>978-1-4051-0679-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Blackwell+dictionary+of+Western+philosophy&rft.pages=266&rft.pub=Wiley-Blackwell&rft.date=2004&rft.isbn=978-1-4051-0679-5&rft.au=Nicholas+Bunnin&rft.au=Jiyuan+Yu&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DOskKWI1YA7AC%26pg%3DPA266&rfr_id=info%3Asid%2Fen.wikipedia.org%3AClassical+logic" class="Z3988"></span></span> </li> <li id="cite_note-Gamut1991-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Gamut1991_2-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFL._T._F._Gamut1991" class="citation book cs1"><a href="/wiki/L._T._F._Gamut" title="L. T. F. Gamut">L. T. F. Gamut</a> (1991). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=Z0KhywkpolMC&pg=PA156"><i>Logic, language, and meaning, Volume 1: Introduction to Logic</i></a>. University of Chicago Press. pp. <span class="nowrap">156–</span>157. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-226-28085-1" title="Special:BookSources/978-0-226-28085-1"><bdi>978-0-226-28085-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Logic%2C+language%2C+and+meaning%2C+Volume+1%3A+Introduction+to+Logic&rft.pages=%3Cspan+class%3D%22nowrap%22%3E156-%3C%2Fspan%3E157&rft.pub=University+of+Chicago+Press&rft.date=1991&rft.isbn=978-0-226-28085-1&rft.au=L.+T.+F.+Gamut&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DZ0KhywkpolMC%26pg%3DPA156&rfr_id=info%3Asid%2Fen.wikipedia.org%3AClassical+logic" class="Z3988"></span></span> </li> <li id="cite_note-Kanamori2000-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Kanamori2000_3-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><cite id="CITEREFAkihiro_Kanamori2000" class="citation conference cs1">Akihiro Kanamori (2000). <a rel="nofollow" class="external text" href="https://www.bu.edu/wcp/IntroV6.htm">"Introduction"</a>. <i>Proceedings of the Twentieth World Congress of Philosophy</i>. Vol. 6. Philosophy Documentation Center.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=conference&rft.atitle=Introduction&rft.btitle=Proceedings+of+the+Twentieth+World+Congress+of+Philosophy&rft.pub=Philosophy+Documentation+Center&rft.date=2000&rft.au=Akihiro+Kanamori&rft_id=https%3A%2F%2Fwww.bu.edu%2Fwcp%2FIntroV6.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AClassical+logic" class="Z3988"></span></span> </li> <li id="cite_note-:0-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><a href="/wiki/Stewart_Shapiro" title="Stewart Shapiro">Shapiro, Stewart</a> (2000). Classical Logic. In Stanford Encyclopedia of Philosophy [Web]. Stanford: The Metaphysics Research Lab. Retrieved October 28, 2006, from <a rel="nofollow" class="external free" href="http://plato.stanford.edu/entries/logic-classical/">http://plato.stanford.edu/entries/logic-classical/</a></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><a href="/wiki/Dov_Gabbay" title="Dov Gabbay">Gabbay, Dov</a>, (1994). 'Classical vs non-classical logic'. In D.M. Gabbay, C.J. Hogger, and J.A. Robinson, (Eds), <i>Handbook of Logic in Artificial Intelligence and Logic Programming</i>, volume 2, chapter 2.6. Oxford University Press.</span> </li> <li id="cite_note-haack-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-haack_6-0">^</a></b></span> <span class="reference-text"><a href="/wiki/Susan_Haack" title="Susan Haack">Haack, Susan</a>, (1996). <i>Deviant Logic, Fuzzy Logic: Beyond the Formalism</i>. Chicago: The University of Chicago Press.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Classical_logic&action=edit&section=5" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/20px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/40px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Media related to <a href="https://commons.wikimedia.org/wiki/Category:Classical_logic" class="extiw" title="commons:Category:Classical logic">Classical logic</a> at Wikimedia Commons</li> <li>Warren Goldfarb, "Deductive Logic", 1st edition, 2003, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222" /><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-87220-660-2" title="Special:BookSources/0-87220-660-2">0-87220-660-2</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol 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.navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Classical_logic" title="Template:Classical logic"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Classical_logic" title="Template talk:Classical logic"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Classical_logic" title="Special:EditPage/Template:Classical logic"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Classical_logic61" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">Classical logic</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Quantifier_(logic)" title="Quantifier (logic)">Quantifiers</a></li> <li><a href="/wiki/Predicate_(mathematical_logic)" class="mw-redirect" title="Predicate (mathematical logic)">Predicate</a></li> <li><a href="/wiki/Logical_connective" title="Logical connective">Connective</a></li> <li><a href="/wiki/Tautology_(logic)" title="Tautology (logic)">Tautology</a></li> <li><a href="/wiki/Truth_table" title="Truth table">Truth tables</a></li> <li><a href="/wiki/Truth_function" title="Truth function">Truth function</a></li> <li><a href="/wiki/Truth_value" title="Truth value">Truth value</a></li> <li><a href="/wiki/Well-formed_formula" title="Well-formed formula">Well-formed formula</a></li> <li><a href="/wiki/Logicism" title="Logicism">Logicism</a></li> <li><a href="/wiki/Problem_of_multiple_generality" title="Problem of multiple generality">Problem of multiple generality</a></li> <li><a href="/wiki/Associative_property" title="Associative property">Associativity</a></li> <li><a href="/wiki/Distributive_property" title="Distributive property">Distribution</a></li> <li><a href="/wiki/Validity_(logic)" title="Validity (logic)">Validity</a></li> <li><a href="/wiki/Soundness" title="Soundness">Soundness</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0 0 0 2px"><div><span typeof="mw:File"><a href="/wiki/File:Logic.svg" class="mw-file-description"><img alt="Law of noncontradiction" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Logic.svg/75px-Logic.svg.png" decoding="async" width="75" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Logic.svg/113px-Logic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Logic.svg/150px-Logic.svg.png 2x" data-file-width="85" data-file-height="28" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Classical logics</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Term_logic" title="Term logic">Term</a></li> <li><a href="/wiki/Propositional_calculus" title="Propositional calculus">Propositional</a></li> <li><a href="/wiki/First-order_logic" title="First-order logic">First-order</a></li> <li><a href="/wiki/Second-order_logic" title="Second-order logic">Second-order</a></li> <li><a href="/wiki/Higher-order_logic" title="Higher-order logic">Higher-order</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Principles</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Commutativity_of_conjunction" title="Commutativity of conjunction">Commutativity of conjunction</a></li> <li><a href="/wiki/Law_of_excluded_middle" title="Law of excluded middle">Excluded middle</a></li> <li><a href="/wiki/Principle_of_bivalence" title="Principle of bivalence">Bivalence</a></li> <li><a href="/wiki/Law_of_noncontradiction" title="Law of noncontradiction">Noncontradiction</a></li> <li><a href="/wiki/Monotonicity_of_entailment" title="Monotonicity of entailment">Monotonicity of entailment</a></li> <li><a href="/wiki/Principle_of_explosion" title="Principle of explosion">Explosion</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Rules</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/De_Morgan%27s_laws" title="De Morgan's laws">De Morgan's laws</a></li> <li><a href="/wiki/Material_implication_(rule_of_inference)" title="Material implication (rule of inference)">Material implication</a></li> <li><a href="/wiki/Transposition_(logic)" class="mw-redirect" title="Transposition (logic)">Transposition</a></li> <li><a href="/wiki/Modus_ponens" title="Modus ponens">modus ponens</a></li> <li><a href="/wiki/Modus_tollens" title="Modus tollens">modus tollens</a></li> <li><a href="/wiki/Modus_ponendo_tollens" title="Modus ponendo tollens">modus ponendo tollens</a></li> <li><a href="/wiki/Constructive_dilemma" title="Constructive dilemma">Constructive dilemma</a></li> <li><a href="/wiki/Destructive_dilemma" title="Destructive dilemma">Destructive dilemma</a></li> <li><a href="/wiki/Disjunctive_syllogism" title="Disjunctive syllogism">Disjunctive syllogism</a></li> <li><a href="/wiki/Hypothetical_syllogism" title="Hypothetical syllogism">Hypothetical syllogism</a></li> <li><a href="/wiki/Absorption_(logic)" title="Absorption (logic)">Absorption</a></li></ul> </div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%">Introduction</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Negation_introduction" title="Negation introduction">Negation</a></li> <li><a href="/wiki/Double_negation_introduction" class="mw-redirect" title="Double negation introduction">Double negation</a></li> <li><a href="/wiki/Existential_generalization" title="Existential generalization">Existential</a></li> <li><a href="/wiki/Universal_generalization" title="Universal generalization">Universal</a></li> <li><a href="/wiki/Biconditional_introduction" title="Biconditional introduction">Biconditional</a></li> <li><a href="/wiki/Conjunction_introduction" title="Conjunction introduction">Conjunction</a></li> <li><a href="/wiki/Disjunction_introduction" title="Disjunction introduction">Disjunction</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Elimination</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Double_negation_elimination" class="mw-redirect" title="Double negation elimination">Double negation</a></li> <li><a href="/wiki/Existential_instantiation" title="Existential instantiation">Existential</a></li> <li><a href="/wiki/Universal_instantiation" title="Universal instantiation">Universal</a></li> <li><a href="/wiki/Biconditional_elimination" title="Biconditional elimination">Biconditional</a></li> <li><a href="/wiki/Conjunction_elimination" title="Conjunction elimination">Conjunction</a></li> <li><a href="/wiki/Disjunction_elimination" title="Disjunction elimination">Disjunction</a></li></ul> </div></td></tr></tbody></table><div> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">People</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Bernard_Bolzano" title="Bernard Bolzano">Bernard Bolzano</a></li> <li><a href="/wiki/George_Boole" title="George Boole">George Boole</a></li> <li><a href="/wiki/Georg_Cantor" title="Georg Cantor">Georg Cantor</a></li> <li><a href="/wiki/Richard_Dedekind" title="Richard Dedekind">Richard Dedekind</a></li> <li><a href="/wiki/Augustus_De_Morgan" title="Augustus De Morgan">Augustus De Morgan</a></li> <li><a href="/wiki/Gottlob_Frege" title="Gottlob Frege">Gottlob Frege</a></li> <li><a href="/wiki/Kurt_G%C3%B6del" title="Kurt Gödel">Kurt Gödel</a></li> <li><a href="/wiki/Hugh_MacColl" title="Hugh MacColl">Hugh MacColl</a></li> <li><a href="/wiki/Giuseppe_Peano" title="Giuseppe Peano">Giuseppe Peano</a></li> <li><a href="/wiki/Charles_Sanders_Peirce" title="Charles Sanders Peirce">Charles Sanders Peirce</a></li> <li><a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Bertrand Russell</a></li> <li><a href="/wiki/Ernst_Schr%C3%B6der_(mathematician)" title="Ernst Schröder (mathematician)">Ernst Schröder</a></li> <li><a href="/wiki/Henry_M._Sheffer" title="Henry M. Sheffer">Henry M. Sheffer</a></li> <li><a href="/wiki/Alfred_Tarski" title="Alfred Tarski">Alfred Tarski</a></li> <li><a href="/wiki/Willard_Van_Orman_Quine" title="Willard Van Orman Quine">Willard Van Orman Quine</a></li> <li><a href="/wiki/Ludwig_Wittgenstein" title="Ludwig Wittgenstein">Ludwig Wittgenstein</a></li> <li><a href="/wiki/Jan_%C5%81ukasiewicz" title="Jan Łukasiewicz">Jan Łukasiewicz</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Works</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Begriffsschrift" title="Begriffsschrift">Begriffsschrift</a></li> <li><a href="/wiki/Function_and_Concept" title="Function and Concept">Function and Concept</a></li> <li><a href="/wiki/The_Principles_of_Mathematics" title="The Principles of Mathematics">The Principles of Mathematics</a></li> <li><a href="/wiki/Principia_Mathematica" title="Principia Mathematica">Principia Mathematica</a></li> <li><a href="/wiki/Tractatus_Logico-Philosophicus" title="Tractatus Logico-Philosophicus">Tractatus Logico-Philosophicus</a></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236075235" /></div><div role="navigation" class="navbox" aria-labelledby="Mathematical_logic326" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239400231" /><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Mathematical_logic" title="Template:Mathematical logic"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Mathematical_logic" title="Template talk:Mathematical logic"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Mathematical_logic" title="Special:EditPage/Template:Mathematical logic"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Mathematical_logic326" style="font-size:114%;margin:0 4em"><a href="/wiki/Mathematical_logic" title="Mathematical logic">Mathematical logic</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">General</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Axiom" title="Axiom">Axiom</a> <ul><li><a href="/wiki/List_of_axioms" title="List of axioms">list</a></li></ul></li> <li><a href="/wiki/Cardinality" title="Cardinality">Cardinality</a></li> <li><a href="/wiki/First-order_logic" title="First-order logic">First-order logic</a></li> <li><a href="/wiki/Formal_proof" title="Formal proof">Formal proof</a></li> <li><a href="/wiki/Formal_semantics_(logic)" class="mw-redirect" title="Formal semantics (logic)">Formal semantics</a></li> <li><a href="/wiki/Foundations_of_mathematics" title="Foundations of mathematics">Foundations of mathematics</a></li> <li><a href="/wiki/Information_theory" title="Information theory">Information theory</a></li> <li><a href="/wiki/Lemma_(mathematics)" title="Lemma (mathematics)">Lemma</a></li> <li><a href="/wiki/Logical_consequence" title="Logical consequence">Logical consequence</a></li> <li><a href="/wiki/Structure_(mathematical_logic)" title="Structure (mathematical logic)">Model</a></li> <li><a href="/wiki/Theorem" title="Theorem">Theorem</a></li> <li><a href="/wiki/Theory_(mathematical_logic)" title="Theory (mathematical logic)">Theory</a></li> <li><a href="/wiki/Type_theory" title="Type theory">Type theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Theorems (<a href="/wiki/Category:Theorems_in_the_foundations_of_mathematics" title="Category:Theorems in the foundations of mathematics">list</a>)<br /> and <a href="/wiki/Paradoxes_of_set_theory" title="Paradoxes of set theory">paradoxes</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/G%C3%B6del%27s_completeness_theorem" title="Gödel's completeness theorem">Gödel's completeness</a> and <a href="/wiki/G%C3%B6del%27s_incompleteness_theorems" title="Gödel's incompleteness theorems">incompleteness theorems</a></li> <li><a href="/wiki/Tarski%27s_undefinability_theorem" title="Tarski's undefinability theorem">Tarski's undefinability</a></li> <li><a href="/wiki/Banach%E2%80%93Tarski_paradox" title="Banach–Tarski paradox">Banach–Tarski paradox</a></li> <li>Cantor's <a href="/wiki/Cantor%27s_theorem" title="Cantor's theorem">theorem,</a> <a href="/wiki/Cantor%27s_paradox" title="Cantor's paradox">paradox</a> and <a href="/wiki/Cantor%27s_diagonal_argument" title="Cantor's diagonal argument">diagonal argument</a></li> <li><a href="/wiki/Compactness_theorem" title="Compactness theorem">Compactness</a></li> <li><a href="/wiki/Halting_problem" title="Halting problem">Halting problem</a></li> <li><a href="/wiki/Lindstr%C3%B6m%27s_theorem" title="Lindström's theorem">Lindström's</a></li> <li><a href="/wiki/L%C3%B6wenheim%E2%80%93Skolem_theorem" title="Löwenheim–Skolem theorem">Löwenheim–Skolem</a></li> <li><a href="/wiki/Russell%27s_paradox" title="Russell's paradox">Russell's paradox</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Logic" title="Logic">Logics</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="Traditional95" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Term_logic" title="Term logic">Traditional</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a class="mw-selflink selflink">Classical logic</a></li> <li><a href="/wiki/Logical_truth" title="Logical truth">Logical truth</a></li> <li><a href="/wiki/Tautology_(logic)" title="Tautology (logic)">Tautology</a></li> <li><a href="/wiki/Proposition" title="Proposition">Proposition</a></li> <li><a href="/wiki/Inference" title="Inference">Inference</a></li> <li><a href="/wiki/Logical_equivalence" title="Logical equivalence">Logical equivalence</a></li> <li><a href="/wiki/Consistency" title="Consistency">Consistency</a> <ul><li><a href="/wiki/Equiconsistency" title="Equiconsistency">Equiconsistency</a></li></ul></li> <li><a href="/wiki/Argument" title="Argument">Argument</a></li> <li><a href="/wiki/Soundness" title="Soundness">Soundness</a></li> <li><a href="/wiki/Validity_(logic)" title="Validity (logic)">Validity</a></li> <li><a href="/wiki/Syllogism" title="Syllogism">Syllogism</a></li> <li><a href="/wiki/Square_of_opposition" title="Square of opposition">Square of opposition</a></li> <li><a href="/wiki/Venn_diagram" title="Venn diagram">Venn diagram</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Propositional_calculus" title="Propositional calculus">Propositional</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Boolean_algebra" title="Boolean algebra">Boolean algebra</a></li> <li><a href="/wiki/Boolean_function" title="Boolean function">Boolean functions</a></li> <li><a href="/wiki/Logical_connective" title="Logical connective">Logical connectives</a></li> <li><a href="/wiki/Propositional_calculus" title="Propositional calculus">Propositional calculus</a></li> <li><a href="/wiki/Propositional_formula" title="Propositional formula">Propositional formula</a></li> <li><a href="/wiki/Truth_table" title="Truth table">Truth tables</a></li> <li><a href="/wiki/Many-valued_logic" title="Many-valued logic">Many-valued logic</a> <ul><li><a href="/wiki/Three-valued_logic" title="Three-valued logic">3</a></li> <li><a href="/wiki/Finite-valued_logic" title="Finite-valued logic">finite</a></li> <li><a href="/wiki/Infinite-valued_logic" title="Infinite-valued logic">∞</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Predicate_logic" class="mw-redirect" title="Predicate logic">Predicate</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/First-order_logic" title="First-order logic">First-order</a> <ul><li><a href="/wiki/List_of_first-order_theories" title="List of first-order theories"><span style="font-size: 85%;">list</span></a></li></ul></li> <li><a href="/wiki/Second-order_logic" title="Second-order logic">Second-order</a> <ul><li><a href="/wiki/Monadic_second-order_logic" title="Monadic second-order logic">Monadic</a></li></ul></li> <li><a href="/wiki/Higher-order_logic" title="Higher-order logic">Higher-order</a></li> <li><a href="/wiki/Fixed-point_logic" title="Fixed-point logic">Fixed-point</a></li> <li><a href="/wiki/Free_logic" title="Free logic">Free</a></li> <li><a href="/wiki/Quantifier_(logic)" title="Quantifier (logic)">Quantifiers</a></li> <li><a href="/wiki/Predicate_(mathematical_logic)" class="mw-redirect" title="Predicate (mathematical logic)">Predicate</a></li> <li><a href="/wiki/Monadic_predicate_calculus" title="Monadic predicate calculus">Monadic predicate calculus</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Set_theory" title="Set theory">Set theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Zermelo%E2%80%93Fraenkel_set_theory" title="Zermelo–Fraenkel set theory">Set</a> <ul><li><a href="/wiki/Hereditary_set" title="Hereditary set">hereditary</a></li></ul></li> <li><a href="/wiki/Class_(set_theory)" title="Class (set theory)">Class</a></li> <li>(<a href="/wiki/Urelement" title="Urelement">Ur-</a>)<a href="/wiki/Element_(mathematics)" title="Element (mathematics)">Element</a></li> <li><a href="/wiki/Ordinal_number" title="Ordinal number">Ordinal number</a></li> <li><a href="/wiki/Extensionality" title="Extensionality">Extensionality</a></li> <li><a href="/wiki/Forcing_(mathematics)" title="Forcing (mathematics)">Forcing</a></li> <li><a href="/wiki/Relation_(mathematics)" title="Relation (mathematics)">Relation</a> <ul><li><a href="/wiki/Equivalence_relation" title="Equivalence relation">equivalence</a></li> <li><a href="/wiki/Partition_of_a_set" title="Partition of a set">partition</a></li></ul></li> <li>Set operations: <ul><li><a href="/wiki/Intersection_(set_theory)" title="Intersection (set theory)">intersection</a></li> <li><a href="/wiki/Union_(set_theory)" title="Union (set theory)">union</a></li> <li><a href="/wiki/Complement_(set_theory)" title="Complement (set theory)">complement</a></li> <li><a href="/wiki/Cartesian_product" title="Cartesian product">Cartesian product</a></li> <li><a href="/wiki/Power_set" title="Power set">power set</a></li> <li><a href="/wiki/List_of_set_identities_and_relations" title="List of set identities and relations">identities</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Types of <a href="/wiki/Set_(mathematics)" title="Set (mathematics)">sets</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Countable_set" title="Countable set">Countable</a></li> <li><a href="/wiki/Uncountable_set" title="Uncountable set">Uncountable</a></li> <li><a href="/wiki/Empty_set" title="Empty set">Empty</a></li> <li><a href="/wiki/Inhabited_set" title="Inhabited set">Inhabited</a></li> <li><a href="/wiki/Singleton_(mathematics)" title="Singleton (mathematics)">Singleton</a></li> <li><a href="/wiki/Finite_set" title="Finite set">Finite</a></li> <li><a href="/wiki/Infinite_set" title="Infinite set">Infinite</a></li> <li><a href="/wiki/Transitive_set" title="Transitive set">Transitive</a></li> <li><a href="/wiki/Ultrafilter_(set_theory)" class="mw-redirect" title="Ultrafilter (set theory)">Ultrafilter</a></li> <li><a href="/wiki/Recursive_set" class="mw-redirect" title="Recursive set">Recursive</a></li> <li><a href="/wiki/Fuzzy_set" title="Fuzzy set">Fuzzy</a></li> <li><a href="/wiki/Universal_set" title="Universal set">Universal</a></li> <li><a href="/wiki/Universe_(mathematics)" title="Universe (mathematics)">Universe</a> <ul><li><a href="/wiki/Constructible_universe" title="Constructible universe">constructible</a></li> <li><a href="/wiki/Grothendieck_universe" title="Grothendieck universe">Grothendieck</a></li> <li><a href="/wiki/Von_Neumann_universe" title="Von Neumann universe">Von Neumann</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Map_(mathematics)" title="Map (mathematics)">Maps</a> and <a href="/wiki/Cardinality" title="Cardinality">cardinality</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Function_(mathematics)" title="Function (mathematics)">Function</a>/<a href="/wiki/Map_(mathematics)" title="Map (mathematics)">Map</a> <ul><li><a href="/wiki/Domain_of_a_function" title="Domain of a function">domain</a></li> <li><a href="/wiki/Codomain" title="Codomain">codomain</a></li> <li><a href="/wiki/Image_(mathematics)" title="Image (mathematics)">image</a></li></ul></li> <li><a href="/wiki/Injective_function" title="Injective function">In</a>/<a href="/wiki/Surjective_function" title="Surjective function">Sur</a>/<a href="/wiki/Bijection" title="Bijection">Bi</a>-jection</li> <li><a href="/wiki/Schr%C3%B6der%E2%80%93Bernstein_theorem" title="Schröder–Bernstein theorem">Schröder–Bernstein theorem</a></li> <li><a href="/wiki/Isomorphism" title="Isomorphism">Isomorphism</a></li> <li><a href="/wiki/G%C3%B6del_numbering" title="Gödel numbering">Gödel numbering</a></li> <li><a href="/wiki/Enumeration" title="Enumeration">Enumeration</a></li> <li><a href="/wiki/Large_cardinal" title="Large cardinal">Large cardinal</a> <ul><li><a href="/wiki/Inaccessible_cardinal" title="Inaccessible cardinal">inaccessible</a></li></ul></li> <li><a href="/wiki/Aleph_number" title="Aleph number">Aleph number</a></li> <li><a href="/wiki/Operation_(mathematics)" title="Operation (mathematics)">Operation</a> <ul><li><a href="/wiki/Binary_operation" title="Binary operation">binary</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Set theories</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Zermelo%E2%80%93Fraenkel_set_theory" title="Zermelo–Fraenkel set theory">Zermelo–Fraenkel</a> <ul><li><a href="/wiki/Axiom_of_choice" title="Axiom of choice">axiom of choice</a></li> <li><a href="/wiki/Continuum_hypothesis" title="Continuum hypothesis">continuum hypothesis</a></li></ul></li> <li><a href="/wiki/General_set_theory" title="General set theory">General</a></li> <li><a href="/wiki/Kripke%E2%80%93Platek_set_theory" title="Kripke–Platek set theory">Kripke–Platek</a></li> <li><a href="/wiki/Morse%E2%80%93Kelley_set_theory" title="Morse–Kelley set theory">Morse–Kelley</a></li> <li><a href="/wiki/Naive_set_theory" title="Naive set theory">Naive</a></li> <li><a href="/wiki/New_Foundations" title="New Foundations">New Foundations</a></li> <li><a href="/wiki/Tarski%E2%80%93Grothendieck_set_theory" title="Tarski–Grothendieck set theory">Tarski–Grothendieck</a></li> <li><a href="/wiki/Von_Neumann%E2%80%93Bernays%E2%80%93G%C3%B6del_set_theory" title="Von Neumann–Bernays–Gödel set theory">Von Neumann–Bernays–Gödel</a></li> <li><a href="/wiki/Ackermann_set_theory" title="Ackermann set theory">Ackermann</a></li> <li><a href="/wiki/Constructive_set_theory" title="Constructive set theory">Constructive</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Formal_system" title="Formal system">Formal systems</a> (<a href="/wiki/List_of_formal_systems" title="List of formal systems"><span style="font-size: 85%;">list</span></a>),<br /><a href="/wiki/Formal_language" title="Formal language">language</a> and <a href="/wiki/Syntax_(logic)" title="Syntax (logic)">syntax</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Alphabet_(formal_languages)" title="Alphabet (formal languages)">Alphabet</a></li> <li><a href="/wiki/Arity" title="Arity">Arity</a></li> <li><a href="/wiki/Automata_theory" title="Automata theory">Automata</a></li> <li><a href="/wiki/Axiom_schema" title="Axiom schema">Axiom schema</a></li> <li><a href="/wiki/Expression_(mathematics)" title="Expression (mathematics)">Expression</a> <ul><li><a href="/wiki/Ground_expression" title="Ground expression">ground</a></li></ul></li> <li><a href="/wiki/Extension_by_new_constant_and_function_names" title="Extension by new constant and function names">Extension</a> <ul><li><a href="/wiki/Extension_by_definitions" title="Extension by definitions">by definition</a></li> <li><a href="/wiki/Conservative_extension" title="Conservative extension">conservative</a></li></ul></li> <li><a href="/wiki/Finitary_relation" title="Finitary relation">Relation</a></li> <li><a href="/wiki/Formation_rule" title="Formation rule">Formation rule</a></li> <li><a href="/wiki/Formal_grammar" title="Formal grammar">Grammar</a></li> <li><a href="/wiki/Well-formed_formula" title="Well-formed formula">Formula</a> <ul><li><a href="/wiki/Atomic_formula" title="Atomic formula">atomic</a></li> <li><a href="/wiki/Sentence_(mathematical_logic)" title="Sentence (mathematical logic)">closed</a></li> <li><a href="/wiki/Ground_formula" class="mw-redirect" title="Ground formula">ground</a></li> <li><a href="/wiki/Open_formula" title="Open formula">open</a></li></ul></li> <li><a href="/wiki/Free_variables_and_bound_variables" title="Free variables and bound variables">Free/bound variable</a></li> <li><a href="/wiki/Formal_language" title="Formal language">Language</a></li> <li><a href="/wiki/Metalanguage" title="Metalanguage">Metalanguage</a></li> <li><a href="/wiki/Logical_connective" title="Logical connective">Logical connective</a> <ul><li><a href="/wiki/Negation" title="Negation">¬</a></li> <li><a href="/wiki/Logical_disjunction" title="Logical disjunction">∨</a></li> <li><a href="/wiki/Logical_conjunction" title="Logical conjunction">∧</a></li> <li><a href="/wiki/Material_conditional" title="Material conditional">→</a></li> <li><a href="/wiki/Logical_biconditional" title="Logical biconditional">↔</a></li> <li><a href="/wiki/Logical_equality" title="Logical equality">=</a></li></ul></li> <li><a href="/wiki/Predicate_(mathematical_logic)" class="mw-redirect" title="Predicate (mathematical logic)">Predicate</a> <ul><li><a href="/wiki/Functional_predicate" title="Functional predicate">functional</a></li> <li><a href="/wiki/Predicate_variable" title="Predicate variable">variable</a></li> <li><a href="/wiki/Propositional_variable" title="Propositional variable">propositional variable</a></li></ul></li> <li><a href="/wiki/Formal_proof" title="Formal proof">Proof</a></li> <li><a href="/wiki/Quantifier_(logic)" title="Quantifier (logic)">Quantifier</a> <ul><li><a href="/wiki/Existential_quantification" title="Existential quantification">∃</a></li> <li><a href="/wiki/Uniqueness_quantification" title="Uniqueness quantification">!</a></li> <li><a href="/wiki/Universal_quantification" title="Universal quantification">∀</a></li> <li><a href="/wiki/Quantifier_rank" title="Quantifier rank">rank</a></li></ul></li> <li><a href="/wiki/Sentence_(mathematical_logic)" title="Sentence (mathematical logic)">Sentence</a> <ul><li><a href="/wiki/Atomic_sentence" title="Atomic sentence">atomic</a></li> <li><a href="/wiki/Spectrum_of_a_sentence" title="Spectrum of a sentence">spectrum</a></li></ul></li> <li><a href="/wiki/Signature_(logic)" title="Signature (logic)">Signature</a></li> <li><a href="/wiki/String_(formal_languages)" class="mw-redirect" title="String (formal languages)">String</a></li> <li><a href="/wiki/Substitution_(logic)" title="Substitution (logic)">Substitution</a></li> <li><a href="/wiki/Symbol_(formal)" title="Symbol (formal)">Symbol</a> <ul><li><a href="/wiki/Uninterpreted_function" title="Uninterpreted function">function</a></li> <li><a href="/wiki/Logical_constant" title="Logical constant">logical/constant</a></li> <li><a href="/wiki/Non-logical_symbol" title="Non-logical symbol">non-logical</a></li> <li><a href="/wiki/Variable_(mathematics)" title="Variable (mathematics)">variable</a></li></ul></li> <li><a href="/wiki/Term_(logic)" title="Term (logic)">Term</a></li> <li><a href="/wiki/Theory_(mathematical_logic)" title="Theory (mathematical logic)">Theory</a> <ul><li><a href="/wiki/List_of_mathematical_theories" title="List of mathematical theories"><span style="font-size: 85%;">list</span></a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><span class="nowrap">Example <a href="/wiki/Axiomatic_system" title="Axiomatic system">axiomatic<br />systems</a> <span style="font-size: 85%;">(<a href="/wiki/List_of_first-order_theories" title="List of first-order theories">list</a>)</span></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li>of <a href="/wiki/True_arithmetic" title="True arithmetic">arithmetic</a>: <ul><li><a href="/wiki/Peano_axioms" title="Peano axioms">Peano</a></li> <li><a href="/wiki/Second-order_arithmetic" title="Second-order arithmetic">second-order</a></li> <li><a href="/wiki/Elementary_function_arithmetic" title="Elementary function arithmetic">elementary function</a></li> <li><a href="/wiki/Primitive_recursive_arithmetic" title="Primitive recursive arithmetic">primitive recursive</a></li> <li><a href="/wiki/Robinson_arithmetic" title="Robinson arithmetic">Robinson</a></li> <li><a href="/wiki/Skolem_arithmetic" title="Skolem arithmetic">Skolem</a></li></ul></li> <li>of the <a href="/wiki/Construction_of_the_real_numbers" title="Construction of the real numbers">real numbers</a> <ul><li><a href="/wiki/Tarski%27s_axiomatization_of_the_reals" title="Tarski's axiomatization of the reals">Tarski's axiomatization</a></li></ul></li> <li>of <a href="/wiki/Axiomatization_of_Boolean_algebras" class="mw-redirect" title="Axiomatization of Boolean algebras">Boolean algebras</a> <ul><li><a href="/wiki/Boolean_algebras_canonically_defined" title="Boolean algebras canonically defined">canonical</a></li> <li><a href="/wiki/Minimal_axioms_for_Boolean_algebra" title="Minimal axioms for Boolean algebra">minimal axioms</a></li></ul></li> <li>of <a href="/wiki/Foundations_of_geometry" title="Foundations of geometry">geometry</a>: <ul><li><a href="/wiki/Euclidean_geometry" title="Euclidean geometry">Euclidean</a>: <ul><li><a href="/wiki/Euclid%27s_Elements" title="Euclid's Elements"><i>Elements</i></a></li> <li><a href="/wiki/Hilbert%27s_axioms" title="Hilbert's axioms">Hilbert's</a></li> <li><a href="/wiki/Tarski%27s_axioms" title="Tarski's axioms">Tarski's</a></li></ul></li> <li><a href="/wiki/Non-Euclidean_geometry" title="Non-Euclidean geometry">non-Euclidean</a></li></ul></li></ul> <ul><li><i><a href="/wiki/Principia_Mathematica" title="Principia Mathematica">Principia Mathematica</a></i></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Proof_theory" title="Proof theory">Proof theory</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Formal_proof" title="Formal proof">Formal proof</a></li> <li><a href="/wiki/Natural_deduction" title="Natural deduction">Natural deduction</a></li> <li><a href="/wiki/Logical_consequence" title="Logical consequence">Logical consequence</a></li> <li><a href="/wiki/Rule_of_inference" title="Rule of inference">Rule of inference</a></li> <li><a href="/wiki/Sequent_calculus" title="Sequent calculus">Sequent calculus</a></li> <li><a href="/wiki/Theorem" title="Theorem">Theorem</a></li> <li><a href="/wiki/Formal_system" title="Formal system">Systems</a> <ul><li><a href="/wiki/Axiomatic_system" title="Axiomatic system">axiomatic</a></li> <li><a href="/wiki/Deductive_system" class="mw-redirect" title="Deductive system">deductive</a></li> <li><a href="/wiki/Hilbert_system" title="Hilbert system">Hilbert</a> <ul><li><a href="/wiki/List_of_Hilbert_systems" class="mw-redirect" title="List of Hilbert systems">list</a></li></ul></li></ul></li> <li><a href="/wiki/Complete_theory" title="Complete theory">Complete theory</a></li> <li><a href="/wiki/Independence_(mathematical_logic)" title="Independence (mathematical logic)">Independence</a> (<a href="/wiki/List_of_statements_independent_of_ZFC" title="List of statements independent of ZFC">from ZFC</a>)</li> <li><a href="/wiki/Proof_of_impossibility" title="Proof of impossibility">Proof of impossibility</a></li> <li><a href="/wiki/Ordinal_analysis" title="Ordinal analysis">Ordinal analysis</a></li> <li><a href="/wiki/Reverse_mathematics" title="Reverse mathematics">Reverse mathematics</a></li> <li><a href="/wiki/Self-verifying_theories" title="Self-verifying theories">Self-verifying theories</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Model_theory" title="Model theory">Model theory</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Interpretation_(logic)" title="Interpretation (logic)">Interpretation</a> <ul><li><a href="/wiki/Interpretation_function" class="mw-redirect" title="Interpretation function">function</a></li> <li><a href="/wiki/Interpretation_(model_theory)" title="Interpretation (model theory)">of models</a></li></ul></li> <li><a href="/wiki/Structure_(mathematical_logic)" title="Structure (mathematical logic)">Model</a> <ul><li><a href="/wiki/Elementary_equivalence" title="Elementary equivalence">equivalence</a></li> <li><a href="/wiki/Finite_model_theory" title="Finite model theory">finite</a></li> <li><a href="/wiki/Saturated_model" title="Saturated model">saturated</a></li> <li><a href="/wiki/Spectrum_of_a_theory" title="Spectrum of a theory">spectrum</a></li> <li><a href="/wiki/Substructure_(mathematics)" title="Substructure (mathematics)">submodel</a></li></ul></li> <li><a href="/wiki/Non-standard_model" title="Non-standard model">Non-standard model</a> <ul><li><a href="/wiki/Non-standard_model_of_arithmetic" title="Non-standard model of arithmetic">of arithmetic</a></li></ul></li> <li><a href="/wiki/Diagram_(mathematical_logic)" title="Diagram (mathematical logic)">Diagram</a> <ul><li><a href="/wiki/Elementary_diagram" title="Elementary diagram">elementary</a></li></ul></li> <li><a href="/wiki/Categorical_theory" title="Categorical theory">Categorical theory</a></li> <li><a href="/wiki/Model_complete_theory" title="Model complete theory">Model complete theory</a></li> <li><a href="/wiki/Satisfiability" title="Satisfiability">Satisfiability</a></li> <li><a href="/wiki/Semantics_of_logic" title="Semantics of logic">Semantics of logic</a></li> <li><a href="/wiki/Strength_(mathematical_logic)" title="Strength (mathematical logic)">Strength</a></li> <li><a href="/wiki/Theories_of_truth" class="mw-redirect" title="Theories of truth">Theories of truth</a> <ul><li><a href="/wiki/Semantic_theory_of_truth" title="Semantic theory of truth">semantic</a></li> <li><a href="/wiki/Tarski%27s_theory_of_truth" class="mw-redirect" title="Tarski's theory of truth">Tarski's</a></li> <li><a href="/wiki/Kripke%27s_theory_of_truth" class="mw-redirect" title="Kripke's theory of truth">Kripke's</a></li></ul></li> <li><a href="/wiki/T-schema" title="T-schema">T-schema</a></li> <li><a href="/wiki/Transfer_principle" title="Transfer principle">Transfer principle</a></li> <li><a href="/wiki/Truth_predicate" title="Truth predicate">Truth predicate</a></li> <li><a href="/wiki/Truth_value" title="Truth value">Truth value</a></li> <li><a href="/wiki/Type_(model_theory)" title="Type (model theory)">Type</a></li> <li><a href="/wiki/Ultraproduct" title="Ultraproduct">Ultraproduct</a></li> <li><a href="/wiki/Validity_(logic)" title="Validity 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