Generalized quantifier

In formal semantics, a generalized quantifier (GQ) is an expression that denotes a set of sets. This is the standard semantics assigned to quantified noun phrases. For example, the generalized quantifier every boy denotes the set of sets of which every boy is a member:

\{X\mid \forall x(x{\text{ is a boy}}\to x\in X)\}

This treatment of quantifiers has been essential in achieving a compositional semantics for sentences containing quantifiers.

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