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class="firstHeading mw-first-heading"><span class="mw-page-title-main">Montague grammar</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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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">Approach to natural language semantics</div> <p><b>Montague grammar</b> is an approach to <a href="/wiki/Natural_language" title="Natural language">natural language</a> <a href="/wiki/Semantics" title="Semantics">semantics</a>, named after American <a href="/wiki/Logician" class="mw-redirect" title="Logician">logician</a> <a href="/wiki/Richard_Montague" title="Richard Montague">Richard Montague</a>. The Montague grammar is based on <a href="/wiki/Mathematical_logic" title="Mathematical logic">mathematical logic</a>, especially <a href="/wiki/Higher-order_logic" title="Higher-order logic">higher-order</a> <a href="/wiki/Predicate_logic" class="mw-redirect" title="Predicate logic">predicate logic</a> and <a href="/wiki/Lambda_calculus" title="Lambda calculus">lambda calculus</a>, and makes use of the notions of <a href="/wiki/Intensional_logic" title="Intensional logic">intensional logic</a>, via <a href="/wiki/Kripke_semantics" title="Kripke semantics">Kripke models</a>. Montague pioneered this approach in the 1960s and early 1970s. </p> <meta property="mw:PageProp/toc" /> <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=Montague_grammar&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Montague's thesis was that <a href="/wiki/Natural_language" title="Natural language">natural languages</a> (like <a href="/wiki/English_language" title="English language">English</a>) and <a href="/wiki/Formal_language" title="Formal language">formal languages</a> (like <a href="/wiki/Programming_language" title="Programming language">programming languages</a>) can be treated in the same way: </p> <blockquote> <p>There is in my opinion no important theoretical difference between natural languages and the artificial languages of logicians; indeed, I consider it possible to comprehend the syntax and semantics of both kinds of language within a single natural and mathematically precise theory. On this point I differ from a number of philosophers, but agree, I believe, with <a href="/wiki/Noam_Chomsky" title="Noam Chomsky">Chomsky</a> and his associates. ("Universal Grammar" 1970) </p> </blockquote> <p>Montague published what soon became known as Montague grammar<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> in three papers: </p> <ul><li>1970: "<a href="/wiki/Universal_grammar" title="Universal grammar">Universal grammar</a>" (= UG)<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></li> <li>1970: "English as a Formal Language" (= EFL)<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li> <li>1973: "The Proper Treatment of Quantification in Ordinary English" (= PTQ)<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Illustration">Illustration</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Montague_grammar&action=edit&section=2" title="Edit section: Illustration"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Montague grammar can represent the meanings of quite complex sentences compactly. Below is a grammar presented in Eijck and Unger's textbook.<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><p>The types of the syntactic categories in the grammar are as follows, with <i>t</i> denoting a term (a reference to an entity) and <i>f</i> denoting a formula. </p> <table class="wikitable"> <tbody><tr> <th>category </th> <th>symbol </th> <th>type </th></tr> <tr> <td><a href="/wiki/Sentence_(linguistics)" title="Sentence (linguistics)">Sentence</a> </td> <td>S </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> </td></tr> <tr> <td><a href="/wiki/Verb_phrase" title="Verb phrase">Verb phrase</a> </td> <td>VP </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t\rightarrow f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo stretchy="false">→</mo> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t\rightarrow f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da47e8cd703f79a00452fcc0c4863a7f72ae004b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.732ex; height:2.509ex;" alt="{\displaystyle t\rightarrow f}"></span> </td></tr> <tr> <td><a href="/wiki/Noun_phrase" title="Noun phrase">Noun phrase</a> </td> <td>NP </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (t\rightarrow f)\rightarrow f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">→</mo> <mi>f</mi> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (t\rightarrow f)\rightarrow f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ca41ea2ad3aaca7b8c5e5012ab5c8901e5c1d323" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.434ex; height:2.843ex;" alt="{\displaystyle (t\rightarrow f)\rightarrow f}"></span> </td></tr> <tr> <td><a href="/wiki/Common_noun" class="mw-redirect" title="Common noun">Common noun</a> </td> <td>CN </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t\rightarrow f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo stretchy="false">→</mo> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t\rightarrow f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da47e8cd703f79a00452fcc0c4863a7f72ae004b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.732ex; height:2.509ex;" alt="{\displaystyle t\rightarrow f}"></span> </td></tr> <tr> <td><a href="/wiki/Determiner" title="Determiner">Determiner</a> </td> <td>DET </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (t\rightarrow f)\rightarrow ((t\rightarrow f)\rightarrow f)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">→</mo> <mi>f</mi> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">→</mo> <mi>f</mi> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mi>f</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (t\rightarrow f)\rightarrow ((t\rightarrow f)\rightarrow f)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e325079b82e301724453a63b24131a541d0eed1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.399ex; height:2.843ex;" alt="{\displaystyle (t\rightarrow f)\rightarrow ((t\rightarrow f)\rightarrow f)}"></span> </td></tr> <tr> <td><a href="/wiki/Transitive_verb" title="Transitive verb">Transitive verb</a> </td> <td>TV </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle t\rightarrow (t\rightarrow f)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>t</mi> <mo stretchy="false">→</mo> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">→</mo> <mi>f</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle t\rightarrow (t\rightarrow f)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42ed658ca0eb9b615d0fa03b348e8888af5daf02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.995ex; height:2.843ex;" alt="{\displaystyle t\rightarrow (t\rightarrow f)}"></span> </td></tr> </tbody></table> <p>The meaning of a sentence obtained by the rule <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle S:{\mathit {NP}}\ {\mathit {VP}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>S</mi> <mo>:</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> <mi class="MJX-tex-mathit" mathvariant="italic">P</mi> </mrow> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">V</mi> <mi class="MJX-tex-mathit" mathvariant="italic">P</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle S:{\mathit {NP}}\ {\mathit {VP}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/098137152bcb6793818c332f3dea10aa14689ed2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; margin-right: -0.118ex; width:10.741ex; height:2.176ex;" alt="{\displaystyle S:{\mathit {NP}}\ {\mathit {VP}}}"></span> is obtained by applying the function for NP to the function for VP. </p><p>The types of VP and NP might appear unintuitive because of the question as to the meaning of a noun phrase that is not simply a term. This is because meanings of many noun phrases, such as "the man who whistles", are not just terms in predicate logic, but also include a predicate for the activity, like "whistles", which cannot be represented in the term (consisting of constant and function symbols but not of predicates). So we need some term, for example <i>x</i>, and a formula <i>whistles(x)</i> to refer to the man who whistles. The meaning of verb phrases VP can be expressed with that term, for example stating that a particular <i>x</i> satisfies sleeps(x) <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \wedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1caa4004cb216ef2930bb12fe805a76870caed94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \wedge }"></span> snores(x) (expressed as a function from <i>x</i> to that formula). Now the function associated with NP takes that kind of function and combines it with the formulas needed to express the meaning of the noun phrase. This particular way of stating NP and VP is not the only possible one. </p><p>Key is the meaning of an expression is obtained as a function of its components, either by function application (indicated by boldface parentheses enclosing function and argument) or by constructing a new function from the functions associated with the component. This compositionality makes it possible to assign meanings reliably to arbitrarily complex sentence structures, with auxiliary clauses and many other complications. </p><p>The meanings of other categories of expressions are either similarly <a href="/wiki/Function_application" title="Function application">function applications</a>, or <a href="/wiki/Higher-order_function" title="Higher-order function">higher-order functions</a>. The following are the rules of the grammar, with the first column indicating a <a href="/wiki/Non-terminal_symbol" class="mw-redirect" title="Non-terminal symbol">non-terminal symbol</a>, the second column one possible way of producing that non-terminal from other non-terminals and terminals, and the third column indicating the corresponding meaning. </p> <table class="wikitable"> <tbody><tr> <th> </th> <th> </th> <th>meaning </th></tr> <tr> <td>S </td> <td>NP VP </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {(}}{\mathit {NP}}\ {\mathit {VP}}{\boldsymbol {)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> <mi class="MJX-tex-mathit" mathvariant="italic">P</mi> </mrow> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">V</mi> <mi class="MJX-tex-mathit" mathvariant="italic">P</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {(}}{\mathit {NP}}\ {\mathit {VP}}{\boldsymbol {)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1787d77f74ad477b0de46ee7d1fdbb057ac9b4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.265ex; height:2.843ex;" alt="{\displaystyle {\boldsymbol {(}}{\mathit {NP}}\ {\mathit {VP}}{\boldsymbol {)}}}"></span> </td></tr> <tr> <td>NP </td> <td>name </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda P.{\boldsymbol {(}}P\ name{\boldsymbol {)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>P</mi> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mi>P</mi> <mtext> </mtext> <mi>n</mi> <mi>a</mi> <mi>m</mi> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda P.{\boldsymbol {(}}P\ name{\boldsymbol {)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f9a46b8380124097ba8a592c652e7a6787158aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.288ex; height:2.843ex;" alt="{\displaystyle \lambda P.{\boldsymbol {(}}P\ name{\boldsymbol {)}}}"></span> </td></tr> <tr> <td>NP </td> <td>DET CN </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {(}}{\mathit {DET}}\ {\mathit {CN}}{\boldsymbol {)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> <mi class="MJX-tex-mathit" mathvariant="italic">E</mi> <mi class="MJX-tex-mathit" mathvariant="italic">T</mi> </mrow> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">C</mi> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {(}}{\mathit {DET}}\ {\mathit {CN}}{\boldsymbol {)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/947f989a398de09c60b430ed2632d5537c9c9579" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.045ex; height:2.843ex;" alt="{\displaystyle {\boldsymbol {(}}{\mathit {DET}}\ {\mathit {CN}}{\boldsymbol {)}}}"></span> </td></tr> <tr> <td>NP </td> <td>DET RCN </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\boldsymbol {(}}{\mathit {DET}}\ {\mathit {RCN}}{\boldsymbol {)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> <mi class="MJX-tex-mathit" mathvariant="italic">E</mi> <mi class="MJX-tex-mathit" mathvariant="italic">T</mi> </mrow> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">R</mi> <mi class="MJX-tex-mathit" mathvariant="italic">C</mi> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\boldsymbol {(}}{\mathit {DET}}\ {\mathit {RCN}}{\boldsymbol {)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb275b6933146763e07677ef1b18078906c58fec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.739ex; height:2.843ex;" alt="{\displaystyle {\boldsymbol {(}}{\mathit {DET}}\ {\mathit {RCN}}{\boldsymbol {)}}}"></span> </td></tr> <tr> <td>DET </td> <td>"some" </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda P.\lambda Q.\exists x({\boldsymbol {(}}P\ x{\boldsymbol {)}}\wedge {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>P</mi> <mo>.</mo> <mi>λ</mi> <mi>Q</mi> <mo>.</mo> <mi mathvariant="normal">∃</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mi>P</mi> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mi>Q</mi> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda P.\lambda Q.\exists x({\boldsymbol {(}}P\ x{\boldsymbol {)}}\wedge {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b7f2b68b8e1d7dc059ace79ed83d0da2678b459" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.938ex; height:2.843ex;" alt="{\displaystyle \lambda P.\lambda Q.\exists x({\boldsymbol {(}}P\ x{\boldsymbol {)}}\wedge {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}"></span> </td></tr> <tr> <td>DET </td> <td>"a" </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda P.\lambda Q.\exists x({\boldsymbol {(}}P\ x{\boldsymbol {)}}\wedge {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>P</mi> <mo>.</mo> <mi>λ</mi> <mi>Q</mi> <mo>.</mo> <mi mathvariant="normal">∃</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mi>P</mi> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mi>Q</mi> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda P.\lambda Q.\exists x({\boldsymbol {(}}P\ x{\boldsymbol {)}}\wedge {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b7f2b68b8e1d7dc059ace79ed83d0da2678b459" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.938ex; height:2.843ex;" alt="{\displaystyle \lambda P.\lambda Q.\exists x({\boldsymbol {(}}P\ x{\boldsymbol {)}}\wedge {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}"></span> </td></tr> <tr> <td>DET </td> <td>"every" </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda P.\lambda Q.\forall x({\boldsymbol {(}}P\ x{\boldsymbol {)}}\rightarrow {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>P</mi> <mo>.</mo> <mi>λ</mi> <mi>Q</mi> <mo>.</mo> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mi>P</mi> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo stretchy="false">→</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mi>Q</mi> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda P.\lambda Q.\forall x({\boldsymbol {(}}P\ x{\boldsymbol {)}}\rightarrow {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/224b641f793b6117e829a1fb1d8d1581b2b972cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.97ex; height:2.843ex;" alt="{\displaystyle \lambda P.\lambda Q.\forall x({\boldsymbol {(}}P\ x{\boldsymbol {)}}\rightarrow {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}"></span> </td></tr> <tr> <td>DET </td> <td>"no" </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda P.\lambda Q.\forall x({\boldsymbol {(}}P\ x{\boldsymbol {)}}\rightarrow \neg {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>P</mi> <mo>.</mo> <mi>λ</mi> <mi>Q</mi> <mo>.</mo> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mi>P</mi> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo stretchy="false">→</mo> <mi mathvariant="normal">¬</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mi>Q</mi> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda P.\lambda Q.\forall x({\boldsymbol {(}}P\ x{\boldsymbol {)}}\rightarrow \neg {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/67f513e731315ab35ce1986f2bf2f206b43ccb31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:29.52ex; height:2.843ex;" alt="{\displaystyle \lambda P.\lambda Q.\forall x({\boldsymbol {(}}P\ x{\boldsymbol {)}}\rightarrow \neg {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}"></span> </td></tr> <tr> <td>VP </td> <td>intransverb </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda x.intransverb(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>x</mi> <mo>.</mo> <mi>i</mi> <mi>n</mi> <mi>t</mi> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>s</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>b</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda x.intransverb(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/28ce2122c18f4707389d75472a83a8fc77bcad4c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.916ex; height:2.843ex;" alt="{\displaystyle \lambda x.intransverb(x)}"></span> </td></tr> <tr> <td>VP </td> <td>TV NP </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda x.{\boldsymbol {(}}{\mathit {NP}}\ \lambda y.{\boldsymbol {(}}{\mathit {TV}}\ y\ x{\boldsymbol {)}}{\boldsymbol {)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>x</mi> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> <mi class="MJX-tex-mathit" mathvariant="italic">P</mi> </mrow> </mrow> <mtext> </mtext> <mi>λ</mi> <mi>y</mi> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">T</mi> <mi class="MJX-tex-mathit" mathvariant="italic">V</mi> </mrow> </mrow> <mtext> </mtext> <mi>y</mi> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda x.{\boldsymbol {(}}{\mathit {NP}}\ \lambda y.{\boldsymbol {(}}{\mathit {TV}}\ y\ x{\boldsymbol {)}}{\boldsymbol {)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e7748847cd23a46e48c92dbbf034015d137e81c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.342ex; height:2.843ex;" alt="{\displaystyle \lambda x.{\boldsymbol {(}}{\mathit {NP}}\ \lambda y.{\boldsymbol {(}}{\mathit {TV}}\ y\ x{\boldsymbol {)}}{\boldsymbol {)}}}"></span> </td></tr> <tr> <td>TV </td> <td>transverb </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda y.\lambda x.transverb(x,y)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>y</mi> <mo>.</mo> <mi>λ</mi> <mi>x</mi> <mo>.</mo> <mi>t</mi> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>s</mi> <mi>v</mi> <mi>e</mi> <mi>r</mi> <mi>b</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda y.\lambda x.transverb(x,y)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90e7f7689cf7fbdfbd91f746c5de7270c536e71f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.452ex; height:2.843ex;" alt="{\displaystyle \lambda y.\lambda x.transverb(x,y)}"></span> </td></tr> <tr> <td>RCN </td> <td>CN "that" VP </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda x.({\boldsymbol {(}}{\mathit {CN}}\ x{\boldsymbol {)}}\wedge {\boldsymbol {(}}{\mathit {VP}}\ x{\boldsymbol {)}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>x</mi> <mo>.</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">C</mi> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> </mrow> </mrow> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">V</mi> <mi class="MJX-tex-mathit" mathvariant="italic">P</mi> </mrow> </mrow> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda x.({\boldsymbol {(}}{\mathit {CN}}\ x{\boldsymbol {)}}\wedge {\boldsymbol {(}}{\mathit {VP}}\ x{\boldsymbol {)}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1fe36fbf8f358315ad37242a55a7eba12ffd0cbf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:22.783ex; height:2.843ex;" alt="{\displaystyle \lambda x.({\boldsymbol {(}}{\mathit {CN}}\ x{\boldsymbol {)}}\wedge {\boldsymbol {(}}{\mathit {VP}}\ x{\boldsymbol {)}})}"></span> </td></tr> <tr> <td>RCN </td> <td>CN "that" NP TV </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda x.({\boldsymbol {(}}{\mathit {CN}}\ x{\boldsymbol {)}}\wedge {\boldsymbol {(}}{\mathit {NP}}\ \lambda y.{\boldsymbol {(}}{\mathit {TV}}\ y\ x{\boldsymbol {)}}{\boldsymbol {)}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>x</mi> <mo>.</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">C</mi> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> </mrow> </mrow> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> <mi class="MJX-tex-mathit" mathvariant="italic">P</mi> </mrow> </mrow> <mtext> </mtext> <mi>λ</mi> <mi>y</mi> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">T</mi> <mi class="MJX-tex-mathit" mathvariant="italic">V</mi> </mrow> </mrow> <mtext> </mtext> <mi>y</mi> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda x.({\boldsymbol {(}}{\mathit {CN}}\ x{\boldsymbol {)}}\wedge {\boldsymbol {(}}{\mathit {NP}}\ \lambda y.{\boldsymbol {(}}{\mathit {TV}}\ y\ x{\boldsymbol {)}}{\boldsymbol {)}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6a86c53cd291f8a26612ffb799e297d08a18d024" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.114ex; height:2.843ex;" alt="{\displaystyle \lambda x.({\boldsymbol {(}}{\mathit {CN}}\ x{\boldsymbol {)}}\wedge {\boldsymbol {(}}{\mathit {NP}}\ \lambda y.{\boldsymbol {(}}{\mathit {TV}}\ y\ x{\boldsymbol {)}}{\boldsymbol {)}})}"></span> </td></tr> <tr> <td>CN </td> <td>predicate </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda x.predicate(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>x</mi> <mo>.</mo> <mi>p</mi> <mi>r</mi> <mi>e</mi> <mi>d</mi> <mi>i</mi> <mi>c</mi> <mi>a</mi> <mi>t</mi> <mi>e</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda x.predicate(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/52584b917fc453d50b77db83e747417a6323caaf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.337ex; height:2.843ex;" alt="{\displaystyle \lambda x.predicate(x)}"></span> </td></tr> </tbody></table> <p>Here are example expressions and their associated meaning, according to the above grammar, showing that the meaning of a given sentence is formed from its constituent expressions, either by forming a new higher-order function, or by applying a higher-order function for one expression to the meaning of another. </p> <table class="wikitable"> <tbody><tr> <th>expression </th> <th>meaning </th></tr> <tr> <td>a </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda P.\lambda Q.\exists x({\boldsymbol {(}}P\ x{\boldsymbol {)}}\wedge {\boldsymbol {}}{\boldsymbol {(}}Q\ x{\boldsymbol {)}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>P</mi> <mo>.</mo> <mi>λ</mi> <mi>Q</mi> <mo>.</mo> <mi mathvariant="normal">∃</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mi>P</mi> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mi>Q</mi> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda P.\lambda Q.\exists x({\boldsymbol {(}}P\ x{\boldsymbol {)}}\wedge {\boldsymbol {}}{\boldsymbol {(}}Q\ x{\boldsymbol {)}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58e165feec17f6d4a40f8dfcf80d31c091b79637" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.938ex; height:2.843ex;" alt="{\displaystyle \lambda P.\lambda Q.\exists x({\boldsymbol {(}}P\ x{\boldsymbol {)}}\wedge {\boldsymbol {}}{\boldsymbol {(}}Q\ x{\boldsymbol {)}})}"></span> </td></tr> <tr> <td>man </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda x.{\mathit {MAN}}(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>x</mi> <mo>.</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">M</mi> <mi class="MJX-tex-mathit" mathvariant="italic">A</mi> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda x.{\mathit {MAN}}(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a75bb1926df760b366693eb864a9ed947ccb9dc5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.396ex; height:2.843ex;" alt="{\displaystyle \lambda x.{\mathit {MAN}}(x)}"></span> </td></tr> <tr> <td>a man </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda Q.\exists x({\mathit {MAN}}(x)\wedge {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>Q</mi> <mo>.</mo> <mi mathvariant="normal">∃</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">M</mi> <mi class="MJX-tex-mathit" mathvariant="italic">A</mi> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mi>Q</mi> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda Q.\exists x({\mathit {MAN}}(x)\wedge {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b9d61bdbf9369c556456a117feb3b02472773d97" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:25.746ex; height:2.843ex;" alt="{\displaystyle \lambda Q.\exists x({\mathit {MAN}}(x)\wedge {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}"></span> </td></tr> <tr> <td>sleeps </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda x.SLEEPS(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>x</mi> <mo>.</mo> <mi>S</mi> <mi>L</mi> <mi>E</mi> <mi>E</mi> <mi>P</mi> <mi>S</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda x.SLEEPS(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b890d9147320c598dca93d5e631e1126fc1b6aa2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.736ex; height:2.843ex;" alt="{\displaystyle \lambda x.SLEEPS(x)}"></span> </td></tr> <tr> <td>a man sleeps </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists x({\mathit {MAN}}(x)\wedge {\mathit {SLEEPS}}(x))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∃</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">M</mi> <mi class="MJX-tex-mathit" mathvariant="italic">A</mi> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> <mi class="MJX-tex-mathit" mathvariant="italic">L</mi> <mi class="MJX-tex-mathit" mathvariant="italic">E</mi> <mi class="MJX-tex-mathit" mathvariant="italic">E</mi> <mi class="MJX-tex-mathit" mathvariant="italic">P</mi> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exists x({\mathit {MAN}}(x)\wedge {\mathit {SLEEPS}}(x))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5667b15f95c6ee3e4c43dc8f88aa6c913b71bc0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:27.628ex; height:2.843ex;" alt="{\displaystyle \exists x({\mathit {MAN}}(x)\wedge {\mathit {SLEEPS}}(x))}"></span> </td></tr> <tr> <td>man that dreams </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda x.({\mathit {MAN}}(x)\wedge {\mathit {DREAMS}}(x))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>x</mi> <mo>.</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">M</mi> <mi class="MJX-tex-mathit" mathvariant="italic">A</mi> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> <mi class="MJX-tex-mathit" mathvariant="italic">R</mi> <mi class="MJX-tex-mathit" mathvariant="italic">E</mi> <mi class="MJX-tex-mathit" mathvariant="italic">A</mi> <mi class="MJX-tex-mathit" mathvariant="italic">M</mi> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda x.({\mathit {MAN}}(x)\wedge {\mathit {DREAMS}}(x))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b18b8186d24b786214380a9f70ffac4911e07410" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.07ex; height:2.843ex;" alt="{\displaystyle \lambda x.({\mathit {MAN}}(x)\wedge {\mathit {DREAMS}}(x))}"></span> </td></tr> <tr> <td>a man that dreams </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda Q.\exists x({\mathit {MAN}}(x)\wedge {\mathit {DREAMS}}(x)\wedge {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mi>Q</mi> <mo>.</mo> <mi mathvariant="normal">∃</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">M</mi> <mi class="MJX-tex-mathit" mathvariant="italic">A</mi> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> <mi class="MJX-tex-mathit" mathvariant="italic">R</mi> <mi class="MJX-tex-mathit" mathvariant="italic">E</mi> <mi class="MJX-tex-mathit" mathvariant="italic">A</mi> <mi class="MJX-tex-mathit" mathvariant="italic">M</mi> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">(</mo> </mrow> <mi>Q</mi> <mtext> </mtext> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mo mathvariant="bold" stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda Q.\exists x({\mathit {MAN}}(x)\wedge {\mathit {DREAMS}}(x)\wedge {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21473e5beefd61107366ab49d09a65f53a10b409" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:41.61ex; height:2.843ex;" alt="{\displaystyle \lambda Q.\exists x({\mathit {MAN}}(x)\wedge {\mathit {DREAMS}}(x)\wedge {\boldsymbol {(}}Q\ x{\boldsymbol {)}})}"></span> </td></tr> <tr> <td>a man that dreams sleeps </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists x({\mathit {MAN}}(x)\wedge {\mathit {DREAMS}}(x)\wedge {\mathit {SLEEPS}}(x))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∃</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">M</mi> <mi class="MJX-tex-mathit" mathvariant="italic">A</mi> <mi class="MJX-tex-mathit" mathvariant="italic">N</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">D</mi> <mi class="MJX-tex-mathit" mathvariant="italic">R</mi> <mi class="MJX-tex-mathit" mathvariant="italic">E</mi> <mi class="MJX-tex-mathit" mathvariant="italic">A</mi> <mi class="MJX-tex-mathit" mathvariant="italic">M</mi> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> <mi class="MJX-tex-mathit" mathvariant="italic">L</mi> <mi class="MJX-tex-mathit" mathvariant="italic">E</mi> <mi class="MJX-tex-mathit" mathvariant="italic">E</mi> <mi class="MJX-tex-mathit" mathvariant="italic">P</mi> <mi class="MJX-tex-mathit" mathvariant="italic">S</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exists x({\mathit {MAN}}(x)\wedge {\mathit {DREAMS}}(x)\wedge {\mathit {SLEEPS}}(x))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d94f03688dfcbd94d5bee3569b54f6f0a3af884" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:43.493ex; height:2.843ex;" alt="{\displaystyle \exists x({\mathit {MAN}}(x)\wedge {\mathit {DREAMS}}(x)\wedge {\mathit {SLEEPS}}(x))}"></span> </td></tr> </tbody></table> <p>The following are other examples of sentences translated into the predicate logic by the grammar. </p> <table class="wikitable"> <tbody><tr> <th>sentence </th> <th>translation to logic </th></tr> <tr> <td>Jill sees Jack </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle sees(Jill,Jack)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> <mi>e</mi> <mi>e</mi> <mi>s</mi> <mo stretchy="false">(</mo> <mi>J</mi> <mi>i</mi> <mi>l</mi> <mi>l</mi> <mo>,</mo> <mi>J</mi> <mi>a</mi> <mi>c</mi> <mi>k</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle sees(Jill,Jack)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21c1cac1864b3098a720ac9af9c68df8feaa4b99" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.771ex; height:2.843ex;" alt="{\displaystyle sees(Jill,Jack)}"></span> </td></tr> <tr> <td>every woman sees a man </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall x(woman(x)\rightarrow (\exists y(man(y)\wedge sees(x,y))))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mi>w</mi> <mi>o</mi> <mi>m</mi> <mi>a</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">∃</mi> <mi>y</mi> <mo stretchy="false">(</mo> <mi>m</mi> <mi>a</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mi>s</mi> <mi>e</mi> <mi>e</mi> <mi>s</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall x(woman(x)\rightarrow (\exists y(man(y)\wedge sees(x,y))))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e483685143e88b315b76bd106fd9c2db9a99682e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:44.596ex; height:2.843ex;" alt="{\displaystyle \forall x(woman(x)\rightarrow (\exists y(man(y)\wedge sees(x,y))))}"></span> </td></tr> <tr> <td>every woman sees a man that sleeps </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall x(woman(x)\rightarrow (\exists y(man(y)\wedge sleeps(y)\wedge sees(x,y))))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mi>w</mi> <mi>o</mi> <mi>m</mi> <mi>a</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">→</mo> <mo stretchy="false">(</mo> <mi mathvariant="normal">∃</mi> <mi>y</mi> <mo stretchy="false">(</mo> <mi>m</mi> <mi>a</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mi>s</mi> <mi>l</mi> <mi>e</mi> <mi>e</mi> <mi>p</mi> <mi>s</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mi>s</mi> <mi>e</mi> <mi>e</mi> <mi>s</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall x(woman(x)\rightarrow (\exists y(man(y)\wedge sleeps(y)\wedge sees(x,y))))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0b015914c232c5cef239cce1d80447a950a041f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:56.354ex; height:2.843ex;" alt="{\displaystyle \forall x(woman(x)\rightarrow (\exists y(man(y)\wedge sleeps(y)\wedge sees(x,y))))}"></span> </td></tr> <tr> <td>a woman that eats sees a man that sleeps </td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists x(woman(x)\wedge eats(x)\wedge \exists y(man(y)\wedge sleeps(y)\wedge sees(x,y)))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∃</mi> <mi>x</mi> <mo stretchy="false">(</mo> <mi>w</mi> <mi>o</mi> <mi>m</mi> <mi>a</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mi>e</mi> <mi>a</mi> <mi>t</mi> <mi>s</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mi mathvariant="normal">∃</mi> <mi>y</mi> <mo stretchy="false">(</mo> <mi>m</mi> <mi>a</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mi>s</mi> <mi>l</mi> <mi>e</mi> <mi>e</mi> <mi>p</mi> <mi>s</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mi>s</mi> <mi>e</mi> <mi>e</mi> <mi>s</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exists x(woman(x)\wedge eats(x)\wedge \exists y(man(y)\wedge sleeps(y)\wedge sees(x,y)))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd6a0eeab7887c25919ae991359628ee36a235f9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:63.479ex; height:2.843ex;" alt="{\displaystyle \exists x(woman(x)\wedge eats(x)\wedge \exists y(man(y)\wedge sleeps(y)\wedge sees(x,y)))}"></span> </td></tr> </tbody></table> <div class="mw-heading mw-heading2"><h2 id="In_popular_culture">In popular culture</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Montague_grammar&action=edit&section=3" title="Edit section: In popular culture"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In <a href="/wiki/David_Foster_Wallace" title="David Foster Wallace">David Foster Wallace</a>'s novel <i><a href="/wiki/Infinite_Jest" title="Infinite Jest">Infinite Jest</a></i>, the protagonist Hal Incandenza has written an essay entitled <i>Montague Grammar and the Semantics of Physical Modality</i>. Montague grammar is also referenced explicitly and implicitly several times throughout the book. </p> <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=Montague_grammar&action=edit&section=4" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Categorial_grammar" title="Categorial grammar">Categorial grammar</a> – Family of formalisms in natural language syntax</li> <li><a href="/wiki/Continuation-passing_style" title="Continuation-passing style">Continuation-passing style</a> – Programming style in which control is passed explicitly</li> <li><a href="/wiki/Kripke_semantics" title="Kripke semantics">Kripke semantics</a> – Formal semantics for non-classical logic systems</li> <li><a href="/wiki/Situation_semantics" title="Situation semantics">Situation semantics</a></li> <li><a href="/wiki/Temperature_paradox" title="Temperature paradox">Temperature paradox</a> – Logical paradox</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=Montague_grammar&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text">The linguist <a href="/wiki/Barbara_Partee" class="mw-redirect" title="Barbara Partee">Barbara Partee</a> credibly claims to have invented the term in 1971 “for the system spelled out in Montague's“ UG, EFL and “especially in PTQ”. See her essay <a rel="nofollow" class="external text" href="http://people.umass.edu/partee/docs/BHP_Essay_Feb05.pdf">"Reflections of a Formal Semanticist as of Feb 2005"</a>, p. 14, footnote 36.</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">"Universal grammar". <i><a href="/wiki/Theoria_(philosophy_journal)" title="Theoria (philosophy journal)">Theoria</a></i> 36 (1970), 373–398. (reprinted in Thomason, 1974)</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text">"English as a Formal Language". In: Bruno Visentini (ed.): <i>Linguaggi nella società e nella tecnica</i>. Mailand 1970, 189–223. (reprinted in Thomason, 1974)</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://semantics.uchicago.edu/kennedy/classes/s08/semantics2/montague73.pdf">"The Proper Treatment of Quantification in Ordinary English</a>". In: <a href="/wiki/Jaakko_Hintikka" title="Jaakko Hintikka">Jaakko Hintikka</a>, <a href="/wiki/Julius_Moravcsik" title="Julius Moravcsik">Julius Moravcsik</a>, <a href="/wiki/Patrick_Suppes" title="Patrick Suppes">Patrick Suppes</a> (eds.): <i>Approaches to Natural Language</i>. Dordrecht 1973, 221–242. (reprinted in Thomason, 1974)</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">J. van Eijck and C. Unger. Computational Semantics with Functional Programming. Cambridge University Press, 2010.</span> </li> </ol></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=Montague_grammar&action=edit&section=6" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Richmond Thomason (ed.): <i>Formal Philosophy. Selected Papers by Richard Montague.</i> New Haven, 1974, <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><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-300-02412-6" title="Special:BookSources/0-300-02412-6">0-300-02412-6</a></li> <li>Paul Portner, Barbara H. Partee (eds.): <i><a href="/wiki/Formal_semantics_(linguistics)" class="mw-redirect" title="Formal semantics (linguistics)">Formal Semantics</a>: The Essential Readings</i>, Blackwell, 2002. <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/0-631-21542-5" title="Special:BookSources/0-631-21542-5">0-631-21542-5</a></li> <li><a href="/wiki/David_Dowty" title="David Dowty">D. R. Dowty</a>, R.E. Wall and S. Peters: <i>Introduction to Montague Semantics.</i> <a href="/wiki/Kluwer_Academic_Publishers" class="mw-redirect" title="Kluwer Academic Publishers">Kluwer Academic Publishers</a>, 1981, <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/90-277-1142-9" title="Special:BookSources/90-277-1142-9">90-277-1142-9</a></li> <li><a href="/wiki/Emmon_Bach" title="Emmon Bach">Emmon Bach</a>: <i>Informal Lectures on Formal Semantics.</i> <a href="/wiki/SUNY_Press" title="SUNY Press">SUNY Press</a>, 1989, <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/0-88706-771-9" title="Special:BookSources/0-88706-771-9">0-88706-771-9</a></li> <li><a href="/wiki/Barbara_Partee" class="mw-redirect" title="Barbara Partee">B. H. Partee</a>, <a href="/wiki/Alice_ter_Meulen" title="Alice ter Meulen">A.G.B. ter Meulen</a> and R.E. Wall: <i>Mathematical Methods in Linguistics.</i> <a href="/wiki/Kluwer_Academic_Publishers" class="mw-redirect" title="Kluwer Academic Publishers">Kluwer Academic Publishers</a>, 1990, <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/90-277-2245-5" title="Special:BookSources/90-277-2245-5">90-277-2245-5</a></li> <li><a href="/wiki/Barbara_Partee" class="mw-redirect" title="Barbara Partee">B. H. Partee</a> with Herman Hendriks: <i>Montague Grammar.</i> In: <i>Handbook of Logic and Language</i>, eds. <a href="/wiki/Johan_van_Benthem_(logician)" title="Johan van Benthem (logician)">J.F.A.K. van Benthem</a> and <a href="/wiki/Alice_ter_Meulen" title="Alice ter Meulen">A. G. B. ter Meulen</a> <a href="/wiki/Elsevier" title="Elsevier">Elsevier</a>/<a href="/wiki/MIT_Press" title="MIT Press">MIT Press</a>, 1997, pp. 5–92. <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/0-262-22053-9" title="Special:BookSources/0-262-22053-9">0-262-22053-9</a></li> <li><a rel="nofollow" class="external text" href="http://freevariable.nl/pubs/rep.pdf">Reinhard Muskens Type-logical Semantics</a> to appear in the Routledge Encyclopedia of Philosophy Online (contains an annotated bibliography).</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Montague_grammar&action=edit&section=7" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://www.cs.cmu.edu/afs/cs/project/ai-repository/ai/areas/nlp/parsing/montague/0.html">A Free Montague Parser</a> in a <a href="https://en.wiktionary.org/wiki/nondeterminism" class="extiw" title="wikt:nondeterminism">non-deterministic</a> extension of <a href="/wiki/Common_Lisp" title="Common Lisp">Common Lisp</a>.</li> <li><a rel="nofollow" class="external text" href="http://people.umass.edu/partee/docs/MontagueGrammarElsevier.PDF">Montague Grammar in historical context. / The theory and the substance of Montague grammar. Central principles. / Further developments and controversies.</a> by Barbara H. Partee.</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 ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist 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(natural language)</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Central concepts</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/Principle_of_compositionality" title="Principle of compositionality">Compositionality</a></li> <li><a href="/wiki/Denotation" title="Denotation">Denotation</a></li> <li><a href="/wiki/Entailment_(linguistics)" title="Entailment (linguistics)">Entailment</a></li> <li><a href="/wiki/Extension_(semantics)" title="Extension (semantics)">Extension</a></li> <li><a href="/wiki/Generalized_quantifier" title="Generalized quantifier">Generalized quantifier</a></li> <li><a href="/wiki/Intension" title="Intension">Intension</a></li> <li><a href="/wiki/Logical_form_(linguistics)" title="Logical form (linguistics)">Logical form</a></li> <li><a href="/wiki/Presupposition" title="Presupposition">Presupposition</a></li> <li><a href="/wiki/Proposition" title="Proposition">Proposition</a></li> <li><a href="/wiki/Reference" title="Reference">Reference</a></li> <li><a href="/wiki/Scope_(formal_semantics)" title="Scope (formal semantics)">Scope</a></li> <li><a href="/wiki/Speech_act" title="Speech act">Speech act</a></li> <li><a href="/wiki/Syntax%E2%80%93semantics_interface" title="Syntax–semantics interface">Syntax–semantics interface</a></li> <li><a href="/wiki/Truth-conditional_semantics" title="Truth-conditional semantics">Truth conditions</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Topics</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 scope="row" class="navbox-group" style="width:1%">Areas</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/Anaphora_(linguistics)" title="Anaphora (linguistics)">Anaphora</a></li> <li><a href="/wiki/Ambiguity" title="Ambiguity">Ambiguity</a></li> <li><a href="/wiki/Binding_(linguistics)" title="Binding (linguistics)">Binding</a></li> <li><a href="/wiki/Conditional_sentence" title="Conditional sentence">Conditionals</a></li> <li><a href="/wiki/Definiteness" title="Definiteness">Definiteness</a></li> <li><a href="/wiki/Disjunction" class="mw-redirect" title="Disjunction">Disjunction</a></li> <li><a href="/wiki/Evidentiality" title="Evidentiality">Evidentiality</a></li> <li><a href="/wiki/Focus_(linguistics)" title="Focus (linguistics)">Focus</a></li> <li><a href="/wiki/Indexicality" title="Indexicality">Indexicality</a></li> <li><a href="/wiki/Lexical_semantics" title="Lexical semantics">Lexical semantics</a></li> <li><a href="/wiki/Linguistic_modality" class="mw-redirect" title="Linguistic modality">Modality</a></li> <li><a href="/wiki/Negation" title="Negation">Negation</a></li> <li><a href="/wiki/Propositional_attitudes" class="mw-redirect" title="Propositional attitudes">Propositional attitudes</a></li> <li><a href="/wiki/Tense%E2%80%93aspect%E2%80%93mood" title="Tense–aspect–mood">Tense–aspect–mood</a></li> <li><a href="/wiki/Quantifier_(logic)" title="Quantifier (logic)">Quantification</a></li> <li><a href="/wiki/Vagueness" title="Vagueness">Vagueness</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Phenomena</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/Antecedent-contained_deletion" title="Antecedent-contained deletion">Antecedent-contained deletion</a></li> <li><a href="/wiki/Cataphora" title="Cataphora">Cataphora</a></li> <li><a href="/wiki/Coercion_(linguistics)" title="Coercion (linguistics)">Coercion</a></li> <li><a href="/wiki/Conservativity" title="Conservativity">Conservativity</a></li> <li><a href="/wiki/Counterfactuals" class="mw-redirect" title="Counterfactuals">Counterfactuals</a></li> <li><a href="/wiki/Crossover_effects" title="Crossover effects">Crossover effects</a></li> <li><a href="/wiki/Cumulativity_(linguistics)" title="Cumulativity (linguistics)">Cumulativity</a></li> <li><a href="/wiki/De_dicto_and_de_re" title="De dicto and de re">De dicto and de re</a></li> <li><a href="/wiki/De_se" title="De se">De se</a></li> <li><a href="/wiki/Deontic_modality" title="Deontic modality">Deontic modality</a></li> <li><a href="/wiki/Discourse_relation" title="Discourse relation">Discourse relations</a></li> <li><a href="/wiki/Donkey_anaphora" class="mw-redirect" title="Donkey anaphora">Donkey anaphora</a></li> <li><a href="/wiki/Epistemic_modality" title="Epistemic modality">Epistemic modality</a></li> <li><a href="/wiki/Exhaustivity" title="Exhaustivity">Exhaustivity</a></li> <li><a href="/wiki/Faultless_disagreement" title="Faultless disagreement">Faultless disagreement</a></li> <li><a href="/wiki/Free_choice_inference" title="Free choice inference">Free choice inferences</a></li> <li><a href="/wiki/Givenness" title="Givenness">Givenness</a></li> <li><a href="/wiki/Homogeneity_(linguistics)" class="mw-redirect" title="Homogeneity (linguistics)">Homogeneity (linguistics)</a></li> <li><a href="/wiki/Hurford_disjunction" title="Hurford disjunction">Hurford disjunction</a></li> <li><a href="/wiki/Inalienable_possession" title="Inalienable possession">Inalienable possession</a></li> <li><a href="/wiki/Intersective_modifier" title="Intersective modifier">Intersective modification</a></li> <li><a href="/wiki/Logophoricity" title="Logophoricity">Logophoricity</a></li> <li><a href="/wiki/Mirativity" title="Mirativity">Mirativity</a></li> <li><a href="/wiki/Modal_subordination" title="Modal subordination">Modal subordination</a></li> <li><a href="/wiki/Opaque_context" title="Opaque context">Opaque contexts</a></li> <li><a href="/wiki/Performative_utterance" title="Performative utterance">Performatives</a></li> <li><a href="/wiki/Polarity_item" title="Polarity item">Polarity items</a></li> <li><a href="/wiki/Privative_adjective" title="Privative adjective">Privative adjectives</a></li> <li><a href="/wiki/Quantificational_variability_effect" title="Quantificational variability effect">Quantificational variability effect</a></li> <li><a href="/wiki/Responsive_predicate" title="Responsive predicate">Responsive predicate</a></li> <li><a href="/wiki/Rising_declarative" title="Rising declarative">Rising declaratives</a></li> <li><a href="/wiki/Scalar_implicature" title="Scalar implicature">Scalar implicature</a></li> <li><a href="/wiki/Sloppy_identity" title="Sloppy identity">Sloppy identity</a></li> <li><a href="/wiki/Subsective_modifier" title="Subsective modifier">Subsective modification</a></li> <li><a href="/wiki/Subtrigging" title="Subtrigging">Subtrigging</a></li> <li><a href="/wiki/Telicity" title="Telicity">Telicity</a></li> <li><a href="/wiki/Temperature_paradox" title="Temperature paradox">Temperature paradox</a></li> <li><a href="/wiki/Veridicality" title="Veridicality">Veridicality</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Formalism</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 scope="row" class="navbox-group" style="width:1%">Formal systems</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/Alternative_semantics" title="Alternative semantics">Alternative semantics</a></li> <li><a href="/wiki/Categorial_grammar" title="Categorial grammar">Categorial grammar</a></li> <li><a href="/wiki/Combinatory_categorial_grammar" title="Combinatory categorial grammar">Combinatory categorial grammar</a></li> <li><a href="/wiki/Discourse_representation_theory" title="Discourse representation theory">Discourse representation theory (DRT)</a></li> <li><a href="/wiki/Dynamic_semantics" title="Dynamic semantics">Dynamic semantics</a></li> <li><a href="/wiki/Generative_grammar" title="Generative grammar">Generative grammar</a></li> <li><a href="/wiki/Glue_semantics" title="Glue semantics">Glue semantics</a></li> <li><a href="/wiki/Inquisitive_semantics" title="Inquisitive semantics">Inquisitive semantics</a></li> <li><a href="/wiki/Intensional_logic" title="Intensional logic">Intensional logic</a></li> <li><a href="/wiki/Lambda_calculus" title="Lambda calculus">Lambda calculus</a></li> <li><a href="/wiki/Mereology" title="Mereology">Mereology</a></li> <li><a class="mw-selflink selflink">Montague grammar</a></li> <li><a href="/wiki/Segmented_discourse_representation_theory" class="mw-redirect" title="Segmented discourse representation theory">Segmented discourse representation theory (SDRT)</a></li> <li><a href="/wiki/Situation_semantics" title="Situation semantics">Situation semantics</a></li> <li><a href="/wiki/Supervaluationism" title="Supervaluationism">Supervaluationism</a></li> <li><a href="/wiki/Type_theory" title="Type theory">Type theory</a></li> <li><a href="/wiki/Type_theory_with_records" title="Type theory with records">TTR</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/Autonomy_of_syntax" title="Autonomy of syntax">Autonomy of syntax</a></li> <li><a href="/wiki/Context_set" class="mw-redirect" title="Context set">Context set</a></li> <li><a href="/wiki/Continuation" title="Continuation">Continuation</a></li> <li><a href="/wiki/Conversational_scoreboard" title="Conversational scoreboard">Conversational scoreboard</a></li> <li><a href="/wiki/Downward_entailing" title="Downward entailing">Downward entailing</a></li> <li><a href="/wiki/Existential_closure" title="Existential closure">Existential closure</a></li> <li><a href="/wiki/Function_application" title="Function application">Function application</a></li> <li><a href="/wiki/Meaning_postulate" title="Meaning postulate">Meaning postulate</a></li> <li><a href="/wiki/Monad_(functional_programming)" title="Monad (functional programming)">Monads</a></li> <li><a href="/wiki/Plural_quantification" title="Plural quantification">Plural quantification</a></li> <li><a href="/wiki/Possible_world" title="Possible world">Possible world</a></li> <li><a href="/wiki/Quantifier_raising" class="mw-redirect" title="Quantifier raising">Quantifier raising</a></li> <li><a href="/wiki/Quantization_(linguistics)" title="Quantization (linguistics)">Quantization</a></li> <li><a href="/wiki/Question_under_discussion" title="Question under discussion">Question under discussion</a></li> <li><a href="/wiki/Semantic_parsing" title="Semantic parsing">Semantic parsing</a></li> <li><a href="/wiki/Squiggle_operator" title="Squiggle operator">Squiggle operator</a></li> <li><a href="/wiki/Strawson_entailment" title="Strawson entailment">Strawson entailment</a></li> <li><a href="/wiki/Strict_conditional" title="Strict conditional">Strict conditional</a></li> <li><a href="/wiki/Type_shifter" title="Type shifter">Type shifter</a></li> <li><a href="/wiki/Universal_grinder" title="Universal grinder">Universal grinder</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">See also</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/Cognitive_semantics" title="Cognitive semantics">Cognitive semantics</a></li> <li><a href="/wiki/Computational_semantics" title="Computational semantics">Computational semantics</a></li> <li><a href="/wiki/Distributional_semantics" title="Distributional semantics">Distributional semantics</a></li> <li><a href="/wiki/Formal_grammar" title="Formal grammar">Formal grammar</a></li> <li><a href="/wiki/Inferentialism" class="mw-redirect" title="Inferentialism">Inferentialism</a></li> <li><a href="/wiki/Logic_translation" title="Logic translation">Logic translation</a></li> <li><a href="/wiki/Linguistics_wars" title="Linguistics wars">Linguistics wars</a></li> <li><a href="/wiki/Philosophy_of_language" title="Philosophy of language">Philosophy of language</a></li> <li><a href="/wiki/Pragmatics" title="Pragmatics">Pragmatics</a></li> <li><a href="/wiki/Semantics_of_logic" title="Semantics of logic">Semantics of logic</a></li></ul> </div></td></tr></tbody></table></div>    </div><noscript><img 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