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href="https://el.wikipedia.org/wiki/%CE%A4%CF%85%CF%80%CE%B9%CE%BA%CE%AE_%CF%83%CE%B7%CE%BC%CE%B1%CF%83%CE%B9%CE%BF%CE%BB%CE%BF%CE%B3%CE%AF%CE%B1" title="Τυπική σημασιολογία – Greek" lang="el" hreflang="el" data-title="Τυπική σημασιολογία" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Sem%C3%A1ntica_formal" title="Semántica formal – Spanish" lang="es" hreflang="es" data-title="Semántica formal" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%B9%D9%86%D8%A7%D8%B4%D9%86%D8%A7%D8%B3%DB%8C_%D9%85%D9%86%D8%B7%D9%82%DB%8C" title="معناشناسی منطقی – Persian" lang="fa" hreflang="fa" data-title="معناشناسی منطقی" 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/S%C3%A9mantique_formelle_(logique)" title="Sémantique formelle (logique) – French" lang="fr" hreflang="fr" data-title="Sémantique formelle (logique)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%98%95%EC%8B%9D%EC%9D%98%EB%AF%B8%EB%A1%A0" title="형식의미론 – Korean" lang="ko" hreflang="ko" data-title="형식의미론" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Logikai_szemantika" title="Logikai szemantika – Hungarian" lang="hu" hreflang="hu" data-title="Logikai szemantika" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Formele_semantiek" title="Formele semantiek – Dutch" lang="nl" hreflang="nl" data-title="Formele semantiek" 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%BD%A2%E5%BC%8F%E6%84%8F%E5%91%B3%E8%AB%96" title="形式意味論 – Japanese" lang="ja" hreflang="ja" data-title="形式意味論" 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/Sem%C3%A2ntica_formal_(l%C3%B3gica)" title="Semântica formal (lógica) – Portuguese" lang="pt" hreflang="pt" data-title="Semântica formal (lógica)" 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 href="https://ru.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D1%81%D0%B5%D0%BC%D0%B0%D0%BD%D1%82%D0%B8%D0%BA%D0%B0" title="Логическая семантика – Russian" lang="ru" hreflang="ru" data-title="Логическая семантика" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D0%B5%D0%BC%D0%B0%D0%BD%D1%82%D0%B8%D0%BA%D0%B0_%D0%BB%D0%BE%D0%B3%D1%96%D0%BA%D0%B8" title="Семантика логіки – Ukrainian" lang="uk" hreflang="uk" data-title="Семантика логіки" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%82%8F%E8%BC%AF%E8%AA%9E%E7%BE%A9%E5%AD%B8" title="邏輯語義學 – Cantonese" lang="yue" hreflang="yue" data-title="邏輯語義學" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%82%8F%E8%BC%AF%E8%AA%9E%E7%BE%A9%E5%AD%B8" title="邏輯語義學 – Chinese" lang="zh" hreflang="zh" data-title="邏輯語義學" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q963731#sitelinks-wikipedia" title="Edit interlanguage links" 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.sidebar-navbar{text-align:right;font-size:115%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:640px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}body.skin--responsive .mw-parser-output .sidebar a>img{max-width:none!important}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar sidebar-collapse nomobile nowraplinks hlist"><tbody><tr><td class="sidebar-pretitle">Part of <a href="/wiki/Category:Formal_languages" title="Category:Formal languages"><i>a series</i></a> on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Formal_languages" class="mw-redirect" title="Formal languages">Formal languages</a></th></tr><tr><td class="sidebar-content" style="padding-top:0.2em;"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:#ddddff;text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c">Key concepts</div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Formal_system" title="Formal system">Formal system</a></li> <li><a href="/wiki/Alphabet_(formal_languages)" title="Alphabet (formal languages)">Alphabet</a></li> <li><a href="/wiki/Syntax_(logic)" title="Syntax (logic)">Syntax</a></li> <li><a class="mw-selflink selflink">Formal semantics</a></li> <li><a href="/wiki/Semantics_(computer_science)" title="Semantics (computer science)">Semantics (programming languages)</a></li> <li><a href="/wiki/Formal_grammar" title="Formal grammar">Formal grammar</a></li> <li><a href="/wiki/Formation_rule" title="Formation rule">Formation rule</a></li> <li><a href="/wiki/Well-formed_formula" title="Well-formed formula">Well-formed formula</a></li> <li><a href="/wiki/Automata_theory" title="Automata theory">Automata theory</a></li> <li><a href="/wiki/Regular_expression" title="Regular expression">Regular expression</a></li> <li><a href="/wiki/Production_(computer_science)" title="Production (computer science)">Production</a></li> <li><a href="/wiki/Ground_expression" title="Ground expression">Ground expression</a></li> <li><a href="/wiki/Atomic_formula" title="Atomic formula">Atomic formula</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content" style="padding-top:0.2em;"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:#ddddff;text-align:center;;color: var(--color-base)"><div class="sidebar-list-title-c">Applications</div></div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/Formal_methods" title="Formal methods">Formal methods</a></li> <li><a href="/wiki/Propositional_calculus" title="Propositional calculus">Propositional calculus</a></li> <li><a href="/wiki/Predicate_logic" class="mw-redirect" title="Predicate logic">Predicate logic</a></li> <li><a href="/wiki/Mathematical_notation" title="Mathematical notation">Mathematical notation</a></li> <li><a href="/wiki/Natural_language_processing" title="Natural language processing">Natural language processing</a></li> <li><a href="/wiki/Programming_language_theory" title="Programming language theory">Programming language theory</a></li> <li><a href="/wiki/Computational_linguistics" title="Computational linguistics">Computational linguistics</a></li> <li><a href="/wiki/Syntax_analysis" class="mw-redirect" title="Syntax analysis">Syntax analysis</a></li> <li><a href="/wiki/Formal_verification" title="Formal verification">Formal verification</a></li> <li><a href="/wiki/Automated_theorem_proving" title="Automated theorem proving">Automated theorem proving</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .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:Formal_languages" title="Template:Formal languages"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Template_talk:Formal_languages&action=edit&redlink=1" class="new" title="Template talk:Formal languages (page does not exist)"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Formal_languages" title="Special:EditPage/Template:Formal languages"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>In <a href="/wiki/Logic" title="Logic">logic</a>, the <b>semantics of logic</b> or <b>formal semantics</b> is the study of the semantics, or <a href="/wiki/Interpretation_(logic)" title="Interpretation (logic)">interpretations</a>, of <a href="/wiki/Formal_language" title="Formal language">formal languages</a> and (idealizations of) <a href="/wiki/Natural_language" title="Natural language">natural languages</a> usually trying to capture the pre-theoretic notion of <a href="/wiki/Logical_consequence" title="Logical consequence">logical consequence</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Semantics_of_logic&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Truth_condition" title="Truth condition">truth conditions</a> of various sentences we may encounter in <a href="/wiki/Argument" title="Argument">arguments</a> will depend upon their meaning, and so logicians cannot completely avoid the need to provide some treatment of the meaning of these sentences. The semantics of logic refers to the approaches that logicians have introduced to understand and determine that part of meaning in which they are interested; the logician traditionally is not interested in the sentence as uttered but in the <a href="/wiki/Proposition" title="Proposition">proposition</a>, an idealised sentence suitable for logical manipulation.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (January 2011)">citation needed</span></a></i>]</sup> </p><p>Until the advent of modern logic, <a href="/wiki/Aristotle" title="Aristotle">Aristotle</a>'s <i><a href="/wiki/Organon" title="Organon">Organon</a></i>, especially <i><a href="/wiki/De_Interpretatione" class="mw-redirect" title="De Interpretatione">De Interpretatione</a></i>, provided the basis for understanding the significance of logic. The introduction of <a href="/wiki/Quantification_(logic)" class="mw-redirect" title="Quantification (logic)">quantification</a>, needed to solve the <a href="/wiki/Problem_of_multiple_generality" title="Problem of multiple generality">problem of multiple generality</a>, rendered impossible the kind of subject–predicate analysis that governed Aristotle's account, although there is a renewed interest in <a href="/wiki/Term_logic" title="Term logic">term logic</a>, attempting to find <a href="/wiki/Deductive_system" class="mw-redirect" title="Deductive system">calculi</a> in the spirit of Aristotle's <a href="/wiki/Syllogism" title="Syllogism">syllogisms</a>, but with the generality of modern logics based on the quantifier. </p><p>The main modern approaches to semantics for formal languages are the following: </p> <ul><li>The archetype of <i>model-theoretic semantics</i> is <a href="/wiki/Alfred_Tarski" title="Alfred Tarski">Alfred Tarski</a>'s <a href="/wiki/Semantic_theory_of_truth" title="Semantic theory of truth">semantic theory of truth</a>, based on his <a href="/wiki/T-schema" title="T-schema">T-schema</a>, and is one of the founding concepts of <a href="/wiki/Model_theory" title="Model theory">model theory</a>. This is the most widespread approach, and is based on the idea that the meaning of the various parts of the propositions are given by the possible ways we can give a recursively specified group of interpretation functions from them to some predefined mathematical domains: an <a href="/wiki/Interpretation_(logic)" title="Interpretation (logic)">interpretation</a> of <a href="/wiki/First-order_predicate_logic" class="mw-redirect" title="First-order predicate logic">first-order predicate logic</a> is given by a mapping from terms to a universe of <a href="/wiki/Individual" title="Individual">individuals</a>, and a mapping from propositions to the truth values "true" and "false". Model-theoretic semantics provides the foundations for an approach to the theory of meaning known as <a href="/wiki/Truth-conditional_semantics" title="Truth-conditional semantics">truth-conditional semantics</a>, which was pioneered by <a href="/wiki/Donald_Davidson_(philosopher)" title="Donald Davidson (philosopher)">Donald Davidson</a>. <a href="/wiki/Kripke_semantics" title="Kripke semantics">Kripke semantics</a> introduces innovations, but is broadly in the Tarskian mold.</li> <li><i><a href="/wiki/Proof-theoretic_semantics" title="Proof-theoretic semantics">Proof-theoretic semantics</a></i> associates the meaning of propositions with the roles that they can play in inferences. <a href="/wiki/Gerhard_Gentzen" title="Gerhard Gentzen">Gerhard Gentzen</a>, <a href="/wiki/Dag_Prawitz" title="Dag Prawitz">Dag Prawitz</a> and <a href="/wiki/Michael_Dummett" title="Michael Dummett">Michael Dummett</a> are generally seen as the founders of this approach; it is heavily influenced by <a href="/wiki/Ludwig_Wittgenstein" title="Ludwig Wittgenstein">Ludwig Wittgenstein</a>'s later philosophy, especially his aphorism "meaning is use".</li> <li><i><a href="/wiki/Truth-value_semantics" title="Truth-value semantics">Truth-value semantics</a></i> (also commonly referred to as <i>substitutional quantification</i>) was advocated by <a href="/wiki/Ruth_Barcan_Marcus" title="Ruth Barcan Marcus">Ruth Barcan Marcus</a> for <a href="/wiki/Modal_logic" title="Modal logic">modal logics</a> in the early 1960s and later championed by <a href="/wiki/Jon_Michael_Dunn" title="Jon Michael Dunn">J. Michael Dunn</a>, <a href="/wiki/Nuel_Belnap" title="Nuel Belnap">Nuel Belnap</a>, and Hugues Leblanc for standard first-order logic. <a href="/wiki/James_Garson" title="James Garson">James Garson</a> has given some results in the areas of adequacy for <a href="/wiki/Intensional_logic" title="Intensional logic">intensional logics</a> outfitted with such a semantics. The truth conditions for quantified formulas are given purely in terms of truth with no appeal to domains whatsoever (and hence its name <i>truth-value semantics</i>).</li> <li><i><a href="/wiki/Game_semantics" title="Game semantics">Game semantics</a></i> or <i>game-theoretical semantics</i> made a resurgence mainly due to <a href="/wiki/Jaakko_Hintikka" title="Jaakko Hintikka">Jaakko Hintikka</a> for logics of (finite) <a href="/wiki/Branching_quantifier" title="Branching quantifier">partially ordered quantification</a>, which were originally investigated by <a href="/wiki/Leon_Henkin" title="Leon Henkin">Leon Henkin</a>, who studied <a href="/wiki/Henkin_quantifier" class="mw-redirect" title="Henkin quantifier">Henkin quantifiers</a>.</li> <li><i><a href="/wiki/Probabilistic_semantics" title="Probabilistic semantics">Probabilistic semantics</a></i> originated from <a href="/wiki/Hartry_Field" title="Hartry Field">Hartry Field</a> and has been shown equivalent to and a natural generalization of truth-value semantics. Like truth-value semantics, it is also non-referential in nature.</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Semantics_of_logic&action=edit&section=2" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1266661725">.mw-parser-output .portalbox{padding:0;margin:0.5em 0;display:table;box-sizing:border-box;max-width:175px;list-style:none}.mw-parser-output .portalborder{border:1px solid var(--border-color-base,#a2a9b1);padding:0.1em;background:var(--background-color-neutral-subtle,#f8f9fa)}.mw-parser-output .portalbox-entry{display:table-row;font-size:85%;line-height:110%;height:1.9em;font-style:italic;font-weight:bold}.mw-parser-output .portalbox-image{display:table-cell;padding:0.2em;vertical-align:middle;text-align:center}.mw-parser-output .portalbox-link{display:table-cell;padding:0.2em 0.2em 0.2em 0.3em;vertical-align:middle}@media(min-width:720px){.mw-parser-output .portalleft{margin:0.5em 1em 0.5em 0}.mw-parser-output .portalright{clear:right;float:right;margin:0.5em 0 0.5em 1em}}</style><ul role="navigation" aria-label="Portals" class="noprint portalbox portalborder portalright"> <li class="portalbox-entry"><span class="portalbox-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/18px-Socrates.png" decoding="async" width="18" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/27px-Socrates.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Socrates.png/36px-Socrates.png 2x" data-file-width="326" data-file-height="500" /></span></span></span><span class="portalbox-link"><a href="/wiki/Portal:Philosophy" title="Portal:Philosophy">Philosophy portal</a></span></li></ul> <ul><li><a href="/wiki/Algebraic_semantics_(mathematical_logic)" title="Algebraic semantics (mathematical logic)">Algebraic semantics</a></li> <li><a href="/wiki/Formal_semantics_(natural_language)" title="Formal semantics (natural language)">Formal semantics (natural language)</a></li> <li><a href="/wiki/Semantics_(computer_science)" title="Semantics (computer science)">Semantics (computer science)</a></li></ul> <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=Semantics_of_logic&action=edit&section=3" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Jaakko_Hintikka" title="Jaakko Hintikka">Jaakko Hintikka</a> (2007), <i><a rel="nofollow" class="external text" href="https://books.google.com/books?id=WcDUMaSc7osC&q=semantics">Socratic Epistemology: Explorations of Knowledge-Seeking by Questioning</a></i>, Cambridge: Cambridge University Press.</li> <li><a href="/wiki/Ilkka_Niiniluoto" title="Ilkka Niiniluoto">Ilkka Niiniluoto</a> (1999), <i>Critical Scientific Realism</i>, Oxford: Oxford University Press.</li> <li>John N. Martin (2019), <i><a href="/wiki/The_Cartesian_Semantics_of_the_Port_Royal_Logic" title="The Cartesian Semantics of the Port Royal Logic">The Cartesian Semantics of the Port Royal Logic </a></i>, Routledge.</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374" /><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output 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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 href="/wiki/Classical_logic" title="Classical logic">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 class="mw-selflink selflink">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 (logic)">Validity</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Computability_theory" title="Computability theory">Computability 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/Church_encoding" title="Church encoding">Church encoding</a></li> <li><a href="/wiki/Church%E2%80%93Turing_thesis" title="Church–Turing thesis">Church–Turing thesis</a></li> <li><a href="/wiki/Computably_enumerable_set" title="Computably enumerable set">Computably enumerable</a></li> <li><a href="/wiki/Computable_function" title="Computable function">Computable function</a></li> <li><a href="/wiki/Computable_set" title="Computable set">Computable set</a></li> <li><a href="/wiki/Decision_problem" title="Decision problem">Decision problem</a> <ul><li><a href="/wiki/Decidability_(logic)" title="Decidability (logic)">decidable</a></li> <li><a href="/wiki/Undecidable_problem" title="Undecidable problem">undecidable</a></li> <li><a href="/wiki/P_(complexity)" title="P (complexity)">P</a></li> <li><a href="/wiki/NP_(complexity)" title="NP (complexity)">NP</a></li> <li><a href="/wiki/P_versus_NP_problem" title="P versus NP problem">P versus NP problem</a></li></ul></li> <li><a href="/wiki/Kolmogorov_complexity" title="Kolmogorov complexity">Kolmogorov complexity</a></li> <li><a href="/wiki/Lambda_calculus" title="Lambda calculus">Lambda calculus</a></li> <li><a href="/wiki/Primitive_recursive_function" title="Primitive recursive function">Primitive recursive function</a></li> <li><a href="/wiki/Recursion" title="Recursion">Recursion</a></li> <li><a href="/wiki/Recursive_set" class="mw-redirect" title="Recursive set">Recursive set</a></li> <li><a href="/wiki/Turing_machine" title="Turing machine">Turing machine</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%">Related</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/Abstract_logic" title="Abstract logic">Abstract logic</a></li> <li><a href="/wiki/Algebraic_logic" title="Algebraic logic">Algebraic logic</a></li> <li><a href="/wiki/Automated_theorem_proving" title="Automated theorem proving">Automated theorem proving</a></li> <li><a href="/wiki/Category_theory" title="Category theory">Category theory</a></li> <li><a href="/wiki/Concrete_category" title="Concrete category">Concrete</a>/<a href="/wiki/Category_(mathematics)" title="Category (mathematics)">Abstract category</a></li> <li><a href="/wiki/Category_of_sets" title="Category of sets">Category of sets</a></li> <li><a href="/wiki/History_of_logic" title="History of logic">History of logic</a></li> <li><a href="/wiki/History_of_mathematical_logic" class="mw-redirect" title="History of mathematical logic">History of mathematical logic</a> <ul><li><a href="/wiki/Timeline_of_mathematical_logic" title="Timeline of mathematical logic">timeline</a></li></ul></li> <li><a href="/wiki/Logicism" title="Logicism">Logicism</a></li> <li><a href="/wiki/Mathematical_object" title="Mathematical object">Mathematical object</a></li> <li><a href="/wiki/Philosophy_of_mathematics" title="Philosophy of mathematics">Philosophy of mathematics</a></li> <li><a href="/wiki/Supertask" title="Supertask">Supertask</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><b><span class="nowrap"><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img alt="icon" 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title="Eubulides">Eubulides</a></li> <li><a href="/wiki/Diodorus_Cronus" title="Diodorus Cronus">Diodorus</a></li> <li><a href="/wiki/Chrysippus" title="Chrysippus">Chrysippus</a></li> <li><a href="/wiki/Zhuang_Zhou" title="Zhuang Zhou">Zhuangzi</a></li> <li><a href="/wiki/Xunzi_(philosopher)" title="Xunzi (philosopher)">Xunzi</a></li> <li><a href="/wiki/Averroes" title="Averroes">Averroes</a></li> <li><a href="/wiki/Ibn_Khaldun" title="Ibn Khaldun">Ibn Khaldun</a></li> <li><a href="/wiki/Thomas_Hobbes" title="Thomas Hobbes">Hobbes</a></li> <li><a href="/wiki/John_Wilkins" title="John Wilkins">Wilkins</a></li> <li><a href="/wiki/Antoine_Arnauld" title="Antoine Arnauld">Arnauld</a></li> <li><a href="/wiki/Claude_Lancelot" title="Claude Lancelot">Lancelot</a></li> <li><a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Leibniz</a></li> <li><a href="/wiki/George_Berkeley" title="George Berkeley">Berkeley</a></li> <li><a href="/wiki/Johann_Gottfried_Herder" title="Johann Gottfried Herder">Herder</a></li> <li><a href="/wiki/Wilhelm_von_Humboldt" title="Wilhelm von Humboldt">von Humboldt</a></li> <li><a href="/wiki/Fritz_Mauthner" title="Fritz Mauthner">Mauthner</a></li> <li><a href="/wiki/Paul_Ric%C5%93ur" title="Paul Ricœur">Ricœur</a></li> <li><a href="/wiki/Ferdinand_de_Saussure" title="Ferdinand de Saussure">de Saussure</a></li> <li><a href="/wiki/Gottlob_Frege" title="Gottlob Frege">Frege</a></li> <li><a href="/wiki/Franz_Boas" title="Franz Boas">Boas</a></li> <li><a href="/wiki/Paul_Tillich" title="Paul Tillich">Tillich</a></li> <li><a href="/wiki/Edward_Sapir" title="Edward Sapir">Sapir</a></li> <li><a href="/wiki/Leonard_Bloomfield" title="Leonard Bloomfield">Bloomfield</a></li> <li><a href="/wiki/Henri_Bergson" title="Henri Bergson">Bergson</a></li> <li><a href="/wiki/Lev_Vygotsky" title="Lev Vygotsky">Vygotsky</a></li> <li><a href="/wiki/Ludwig_Wittgenstein" title="Ludwig Wittgenstein">Wittgenstein</a></li> <li><a href="/wiki/Bertrand_Russell" title="Bertrand Russell">Russell</a></li> <li><a href="/wiki/Rudolf_Carnap" title="Rudolf Carnap">Carnap</a></li> <li><a href="/wiki/Jacques_Derrida" title="Jacques Derrida">Derrida</a></li> <li><a href="/wiki/Benjamin_Lee_Whorf" title="Benjamin Lee Whorf">Whorf</a></li> <li><a href="/wiki/J._L._Austin" title="J. L. Austin">Austin</a></li> <li><a href="/wiki/Noam_Chomsky" title="Noam Chomsky">Chomsky</a></li> <li><a href="/wiki/Hans-Georg_Gadamer" title="Hans-Georg Gadamer">Gadamer</a></li> <li><a href="/wiki/Saul_Kripke" title="Saul Kripke">Kripke</a></li> <li><a href="/wiki/A._J._Ayer" title="A. J. Ayer">Ayer</a></li> <li><a href="/wiki/G._E._M._Anscombe" title="G. E. M. Anscombe">Anscombe</a></li> <li><a href="/wiki/Jaakko_Hintikka" title="Jaakko Hintikka">Hintikka</a></li> <li><a href="/wiki/Michael_Dummett" title="Michael Dummett">Dummett</a></li> <li><a href="/wiki/Donald_Davidson_(philosopher)" title="Donald Davidson (philosopher)">Davidson</a></li> <li><a href="/wiki/Paul_Grice" title="Paul Grice">Grice</a></li> <li><a href="/wiki/Gilbert_Ryle" title="Gilbert Ryle">Ryle</a></li> <li><a href="/wiki/P._F._Strawson" title="P. F. Strawson">Strawson</a></li> <li><a href="/wiki/Willard_Van_Orman_Quine" title="Willard Van Orman Quine">Quine</a></li> <li><a href="/wiki/Hilary_Putnam" title="Hilary Putnam">Putnam</a></li> <li><a href="/wiki/David_Lewis_(philosopher)" title="David Lewis (philosopher)">Lewis</a></li> <li><a href="/wiki/John_Searle" title="John Searle">Searle</a></li> <li><a href="/wiki/Paul_Watzlawick" title="Paul Watzlawick">Watzlawick</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Category:Theories_of_language" title="Category:Theories of language">Theories</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/Causal_theory_of_reference" title="Causal theory of reference">Causal theory of reference</a></li> <li><a href="/wiki/Contrastivism" title="Contrastivism">Contrast theory of meaning</a></li> <li><a href="/wiki/Contrastivism" title="Contrastivism">Contrastivism</a></li> <li><a href="/wiki/Conventionalism" title="Conventionalism">Conventionalism</a></li> <li><a href="/wiki/Cratylism" title="Cratylism">Cratylism</a></li> <li><a href="/wiki/Deconstruction" title="Deconstruction">Deconstruction</a></li> <li><a href="/wiki/Descriptivist_theory_of_names" title="Descriptivist theory of names">Descriptivism</a></li> <li><a href="/wiki/Direct_reference_theory" title="Direct reference theory">Direct reference theory</a></li> <li><a href="/wiki/Dramatism" title="Dramatism">Dramatism</a></li> <li><a href="/wiki/Dynamic_semantics" title="Dynamic semantics">Dynamic semantics</a></li> <li><a href="/wiki/Expressivism" title="Expressivism">Expressivism</a></li> <li><a href="/wiki/Inquisitive_semantics" title="Inquisitive semantics">Inquisitive semantics</a></li> <li><a href="/wiki/Linguistic_determinism" title="Linguistic determinism">Linguistic determinism</a></li> <li><a href="/wiki/Mediated_reference_theory" title="Mediated reference theory">Mediated reference theory</a></li> <li><a href="/wiki/Nominalism" title="Nominalism">Nominalism</a></li> <li><a href="/wiki/Non-cognitivism" title="Non-cognitivism">Non-cognitivism</a></li> <li><a href="/wiki/Phallogocentrism" title="Phallogocentrism">Phallogocentrism</a></li> <li><a href="/wiki/Relevance_theory" title="Relevance theory">Relevance theory</a></li> <li><a href="/wiki/Semantic_externalism" title="Semantic externalism">Semantic externalism</a></li> <li><a href="/wiki/Semantic_holism" title="Semantic holism">Semantic holism</a></li> <li><a href="/wiki/Situation_semantics" title="Situation semantics">Situation semantics</a></li> <li><a href="/wiki/Structuralism" title="Structuralism">Structuralism</a></li> <li><a href="/wiki/Supposition_theory" title="Supposition theory">Supposition theory</a></li> <li><a href="/wiki/Symbiosism" title="Symbiosism">Symbiosism</a></li> <li><a href="/wiki/Theological_noncognitivism" title="Theological noncognitivism">Theological noncognitivism</a></li> <li><a href="/wiki/Theory_of_descriptions" title="Theory of descriptions">Theory of descriptions</a> (<a href="/wiki/Definite_description" title="Definite description">Definite description</a>)</li> <li><a href="/wiki/Theory_of_language" title="Theory of language">Theory of language</a></li> <li><a href="/wiki/Unilalianism" title="Unilalianism">Unilalianism</a></li> <li><a href="/wiki/Verificationism" title="Verificationism">Verification theory</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Concepts</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/Ambiguity" title="Ambiguity">Ambiguity</a></li> <li><a href="/wiki/Cant_(language)" title="Cant (language)">Cant</a></li> <li><a href="/wiki/Class_(philosophy)" title="Class (philosophy)">Class</a></li> <li><a href="/wiki/Concept" title="Concept">Concept</a></li> <li><a href="/wiki/Categorization" class="mw-redirect" title="Categorization">Categories</a></li> <li><a href="/wiki/Family_resemblance" title="Family resemblance">Family resemblance</a></li> <li><a href="/wiki/Intension" title="Intension">Intension</a></li> <li><a href="/wiki/Language" title="Language">Language</a></li> <li><a href="/wiki/Linguistic_relativity" title="Linguistic relativity">Linguistic relativity</a></li> <li><a href="/wiki/Logical_form" title="Logical form">Logical form</a></li> <li><a href="/wiki/Mental_representation" title="Mental representation">Mental representation</a></li> <li><a href="/wiki/Metalanguage" title="Metalanguage">Metalanguage</a></li> <li><a href="/wiki/Modality_(natural_language)" class="mw-redirect" title="Modality (natural language)">Modality (natural language)</a></li> <li><a href="/wiki/Presupposition" title="Presupposition">Presupposition</a></li> <li><a href="/wiki/Principle_of_compositionality" title="Principle of compositionality">Principle of compositionality</a></li> <li><a href="/wiki/Property_(philosophy)" title="Property (philosophy)">Property</a></li> <li><a href="/wiki/Proposition" title="Proposition">Proposition</a></li> <li><a href="/wiki/Sense_and_reference" title="Sense and reference">Sense and reference</a></li> <li><a href="/wiki/Sentence_(linguistics)" title="Sentence (linguistics)">Sentence</a></li> <li><a href="/wiki/Set_(mathematics)" title="Set (mathematics)">Set</a></li> <li><a href="/wiki/Sign_(semiotics)" title="Sign (semiotics)">Sign</a></li> <li><a href="/wiki/Speech_act" title="Speech act">Speech act</a></li> <li><a href="/wiki/Statement_(logic)" title="Statement (logic)">Statement</a></li> <li><a href="/wiki/Symbol" title="Symbol">Symbol</a></li> <li><a href="/wiki/Truth-bearer" title="Truth-bearer">Truth-bearer</a></li> <li><a href="/wiki/Use%E2%80%93mention_distinction" title="Use–mention distinction">Use–mention distinction</a></li> <li><i><a href="/wiki/Index_of_philosophy_of_language_articles" title="Index of philosophy of language articles">more...</a></i></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" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><i><a href="/wiki/Cratylus_(dialogue)" title="Cratylus (dialogue)">Cratylus</a></i> <span style="font-size: 85%;">(n.d.)</span></li> <li><i><a href="/wiki/Port-Royal_Grammar" title="Port-Royal Grammar">Port-Royal Grammar</a></i> <span style="font-size: 85%;">(1660)</span></li> <li><i><a href="/wiki/De_Arte_Combinatoria" title="De Arte Combinatoria">De Arte Combinatoria</a></i> <span style="font-size: 85%;">(1666)</span></li> <li><i><a href="/wiki/An_Essay_Towards_a_Real_Character,_and_a_Philosophical_Language" title="An Essay Towards a Real Character, and a Philosophical Language">An Essay Towards a Real Character, and a Philosophical Language</a></i> <span style="font-size: 85%;">(1668)</span></li> <li><i><a href="/wiki/Alciphron_(book)" title="Alciphron (book)">Alciphron</a></i> <span style="font-size: 85%;">(1732)</span></li> <li>"<a href="/wiki/On_Denoting" title="On Denoting">On Denoting</a>" <span style="font-size: 85%;">(1905)</span></li> <li><i><a href="/wiki/Tractatus_Logico-Philosophicus" title="Tractatus Logico-Philosophicus">Tractatus Logico-Philosophicus</a></i> <span style="font-size: 85%;">(1921)</span></li> <li><i><a href="/wiki/Language,_Truth,_and_Logic" title="Language, Truth, and Logic">Language, Truth, and Logic</a></i> <span style="font-size: 85%;">(1936)</span></li> <li><i><a href="/wiki/Two_Dogmas_of_Empiricism" title="Two Dogmas of Empiricism">Two Dogmas of Empiricism</a></i> <span style="font-size: 85%;">(1951)</span></li> <li><i><a href="/wiki/Philosophical_Investigations" title="Philosophical Investigations">Philosophical Investigations</a></i> <span style="font-size: 85%;">(1953)</span></li> <li><i><a href="/wiki/Of_Grammatology" title="Of Grammatology">Of Grammatology</a></i> <span style="font-size: 85%;">(1967)</span></li> <li><i><a href="/wiki/Naming_and_Necessity" title="Naming and Necessity">Naming and Necessity</a></i> <span style="font-size: 85%;">(1980)</span></li> <li><i><a href="/wiki/Wittgenstein_on_Rules_and_Private_Language" title="Wittgenstein on Rules and Private Language">Wittgenstein on Rules and Private Language</a></i> <span style="font-size: 85%;">(1982)</span></li> <li><i><a href="/wiki/Limited_Inc" title="Limited Inc">Limited Inc</a></i> <span style="font-size: 85%;">(1988)</span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related articles</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/Analytic_philosophy" title="Analytic philosophy">Analytic philosophy</a></li> <li><a href="/wiki/Philosophy_of_information" title="Philosophy of information">Philosophy of information</a></li> <li><a href="/wiki/Philosophical_logic" title="Philosophical logic">Philosophical logic</a></li> <li><a href="/wiki/Linguistics" title="Linguistics">Linguistics</a></li> <li><a href="/wiki/Pragmatics" title="Pragmatics">Pragmatics</a></li> <li><a href="/wiki/Rhetoric" title="Rhetoric">Rhetoric</a></li> <li><a href="/wiki/Scholasticism" title="Scholasticism">Scholasticism</a></li> <li><a href="/wiki/School_of_Names" title="School of Names">School of Names</a></li> <li><a href="/wiki/Semantics_(natural_language)" class="mw-redirect" title="Semantics (natural language)">Semantics</a> <ul><li><a href="/wiki/Formal_semantics_(linguistics)" class="mw-redirect" title="Formal semantics (linguistics)">Formal semantics</a></li></ul></li> <li><a href="/wiki/Semiotics" title="Semiotics">Semiotics</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/Category:Philosophy_of_language" 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