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<p>utrecht</p> <p><b>New page</b></p><div>'''Lambda-operator''' is an [[operator]] which makes it possible to construct expressions which denote [[predicate]]s or [[function]]s. Adding the lambda-operator to [[predicate logic]] makes it possible to construct predicates from formulae with free variables.<br /> <br /> === Example ===<br /> <br /> two expressions with lambda-operators are given in (i):<br /> <br /> (i) a lambda x [ kiss(john,x) ]<br /> b lambda x [ man(x) &amp;amp; Neg married(x) ]<br /> <br /> The lambda-expression in (i)a denotes the property of being kissed by John, the one in (i)b denotes the property of being an unmarried man. The lambda-operator plays an important role in [[type logic]], as a mechanism for making functions. If e is an expression of arbitrary type ''b'' and v is a variable of arbitrary type ''a'', then lambda v [ e ] is an expression of type &amp;lt;''a'',''b''&amp;gt;, i.e. a function from things of type ''a'' to things of type ''b''. The lambda-operator makes it possible to give a logical translation of every expression, including quantified noun phrases:<br /> <br /> (ii) a every boy<br /> b lambda P [ All(x) [ boy(x) -&amp;gt; P(x) ]]<br /> <br /> The noun phrase in (ii)a is translated into a logical expression denoting a function from properties to truth values, assigning the value 1 to those properties that every boy has. When we combine the noun phrase in (ii)a with a predicate like ''walk'', then the expression in (ii)b is applied to the translation of ''walk''. In other words: the translation of (iii)a is (iii)b which is logically equivalent with (iii)c (an equivalence which follows from the semantics of the lambda-operator):<br /> <br /> (iii) a Every boy walks<br /> b lambda P [ All(x) [ boy(x) -&amp;gt; P(x) ]] (walk)<br /> c All(x) [ boy(x) -&amp;gt; walk(x) ]<br /> <br /> === Link ===<br /> <br /> [http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Lambda-operator&amp;lemmacode=581 Utrecht Lexicon of Linguistics]<br /> <br /> === References ===<br /> <br /> * Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago.<br /> <br /> {{dc}}<br /> [[Category:Semantics]]</div>

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