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In [[formal semantics (natural language)|formal semantics]], a '''generalized quantifier''' ('''GQ''') is an expression that denotes a [[set of sets]]. This is the standard semantics assigned to [[Quantifier (logic)|quantified]] [[noun phrase]]s. For example, the generalized quantifier ''every boy'' denotes the set of sets of which every boy is a member:
▲:: <math>\{X \,|\, \forall x (x \text{ is a boy} \to x \in X) \}</math>
This treatment of quantifiers has been essential in achieving a [[compositionality|compositional]] [[semantics]] for sentences containing quantifiers.<ref>{{cite book |last1=Montague |first1=Richard |author-link1=Richard Montague |date=1974 |url=http://www.blackwellpublishing.com/content/BPL_Images/Content_store/Sample_chapter/9780631215417/Portner.pdf |chapter=The proper treatment of quantification in English |title=Philosophy, Language, and Artificial Intelligence |series=Studies in Cognitive Systems |volume=2
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