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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>
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