Type logic - Revision history

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'''Type logic''' is a [[logical system]] based on Russell's theory of types. Every expression of a type-logical language belongs to a particular type indicating the set-theoretical [[denotation]] of that expression. There are two basic types, the type e (from [[entity]]) and the type t (from [[truth value]]). The formulas of [[predicate logic]] and [[propositional logic]] are expressions of type t in type logic, denoting truth values; the [[individual constant]]s of predicate logic are expressions of type e in type logic, denoting individuals. All other expressions in type-logic are functional, i.e. they take an expression of type a as their argument and yield an expression of type b, which is indicated in their type as follows: <a,b>. The one-place predicates of predicate logic are of type <e,t> in type logic, denoting a function from entities to truth-values, which is another way to define a set. Two-place predicates are of type <e,<e,t>>. Type logic also allows functions of higher order. Noun modifiers can be treated as expressions of type <<e,t>,<e,t>>, mapping a set into a set. NPs are of type <<e,t>,t>, i.e. functions from sets to truth values, or equivalently, sets of sets. Determiners are relations between sets: <<e,t>,<<e,t>,t>>. In combination with lambda-abstraction, type logic is a very powerful logic for semantic representation. It has been fruitfully applied in [[Montague Grammar]].

=== Links ===

[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Type+logic&lemmacode=200 Utrecht Lexicon of Linguistics]

=== References ===

* Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago.
* Montague, R. 1974. ''Formal philosophy: selected papers of Richard Montague, edited and with an introduction by Richmond H. Thomason,'' Yale University Press, New Haven

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 '''Type logic''' is a [[logical system]] based on Russell's theory of types. Every expression of a type-logical language belongs to a particular type indicating the set-theoretical [[denotation]] of that expression. There are two basic types, the type e (from [[entity]]) and the type t (from [[truth value]]). The formulas of [[predicate logic]] and [[propositional logic]] are expressions of type t in type logic, denoting truth values; the [[individual constant]]s of predicate logic are expressions of type e in type logic, denoting individuals. All other expressions in type-logic are functional, i.e. they take an expression of type a as their argument and yield an expression of type b, which is indicated in their type as follows: &lt;a,b&gt;. The one-place predicates of predicate logic are of type &lt;e,t&gt; in type logic, denoting a function from entities to truth-values, which is another way to define a set. Two-place predicates are of type &lt;e,&lt;e,t&gt;&gt;. Type logic also allows functions of higher order. Noun modifiers can be treated as expressions of type &lt;&lt;e,t&gt;,&lt;e,t&gt;&gt;, mapping a set into a set. NPs are of type &lt;&lt;e,t&gt;,t&gt;, i.e. functions from sets to truth values, or equivalently, sets of sets. Determiners are relations between sets: &lt;&lt;e,t&gt;,&lt;&lt;e,t&gt;,t&gt;&gt;. In combination with lambda-abstraction, type logic is a very powerful logic for semantic representation. It has been fruitfully applied in [[Montague Grammar]].
-=== Links ===
+== Links ==
+*[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Type+logic&lemmacode=200 Utrecht Lexicon of Linguistics]
 * Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago.
 * Montague, R. 1974. ''Formal philosophy: selected papers of Richard Montague, edited and with an introduction by Richmond H. Thomason,'' Yale University Press, New Haven