View source for Quantifier (in predicate logic)

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In [[predicate logic]], the [[logical constant]] indicating whether a statement is universal or particular is calles '''quantifier'''. The [[universal quantifier]] ''All'' indicates that all entities in the universe have a given property while the [[existential quantifier]] ThereIs indicates that at least one entity has the property:

 (i)  a  All(x) [ P(x) ]
         "Every x has property P"
      b  ThereIs(y) [ Q(y) ]
         "At least one y has property Q"

The term quantifier can either be used for the symbols All and ThereIs themselves or for the combination with the variable they bind: All(x) and ThereIs(y). A more complex use of quantifiers is shown in (ii):

 (ii) All(x) [ P(x) -&gt; ThereIs(y) [ Q(y) &amp; R(x,y) ]

which might be the translation of a sentence like ''Every teenage girl adores a rock star''. 


=== Links ===

[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Quantifier&lemmacode=366 Utrecht Lexicon of Linguistics]

=== References ===

* Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago.

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[[Category:Semantics]]