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Reference.org
Generalized quantifier
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<p>In <a href="/facts/Formal_semantics_/FlWb7Hxp">formal semantics</a>, a generalized quantifier (GQ) is an expression that denotes a <a href="/facts/Set_of_sets/WbYof7lP">set of sets</a>. This is the standard semantics assigned to <a href="/facts/Quantifier_(logic)/bgmvwxoo">quantified</a> <a href="/facts/Noun_phrase/mmz3tJt9">noun phrases</a>. For example, the generalized quantifier <i>every boy</i> denotes the set of sets of which every boy is a member: { X ∣ ∀ x ( x is a boy → x ∈ X ) } {\displaystyle \{X\mid \forall x(x{\text{ is a boy}}\to x\in X)\}} </p><p>This treatment of quantifiers has been essential in achieving a <a href="/facts/Compositionality/yP2hR4Le">compositional</a> <a href="/facts/Semantics/1L4WwLAP">semantics</a> for sentences containing quantifiers. </p>