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.^[1]^[2]

^ Montague, Richard (1974). "The proper treatment of quantification in English". In Kulas, J.; Fetzer, J.H.; Rankin, T.L. (eds.). Philosophy, Language, and Artificial Intelligence (PDF). Studies in Cognitive Systems. Vol. 2. Springer, Dordrecht. pp. 141–162. doi:10.1007/978-94-009-2727-8_7. ISBN 978-94-010-7726-2.
^ Barwise, Jon; Cooper, Robin (1981). "Generalized quantifiers and natural language". Linguistics and Philosophy. 4 (2): 159–219. doi:10.1007/BF00350139.

[1] Montague, Richard (1974). "The proper treatment of quantification in English". In Kulas, J.; Fetzer, J.H.; Rankin, T.L. (eds.). Philosophy, Language, and Artificial Intelligence (PDF). Studies in Cognitive Systems. Vol. 2. Springer, Dordrecht. pp. 141–162. doi:10.1007/978-94-009-2727-8_7. ISBN 978-94-010-7726-2.

[Barwise-2] Barwise, Jon; Cooper, Robin (1981). "Generalized quantifiers and natural language". Linguistics and Philosophy. 4 (2): 159–219. doi:10.1007/BF00350139.

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