Generalized quantifier

Summary

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.