Generalized quantifier: Difference between revisions

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In [[linguistics|linguistic]] [[semantics]], a '''generalized quantifier''' ('''GQ''') is an expression that denotes a [[set of sets]]. This is the standard semantics assigned to [[Quantifier (linguistics)|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 \mboxtext{x is a boy} \}to x \subseteqin X) \}</math>

This treatment of quantifiers has been essential in achieving a [[compositionality|compositional]] [[semantics]] for sentences containing quantifiers.<ref> [[Richard Montague|Montague, Richard]]: 1974, '[http://www.blackwellpublishing.com/content/BPL_Images/Content_store/Sample_chapter/9780631215417/Portner.pdf The proper treatment of quantification in English]',