# quantifier

## quantifier

[kwon-tuh-fahy-er]
noun
1.
Logic. an expression, as “all” or “some,” that indicates the quantity of a proposition. Compare existential quantifier, universal quantifier.
2.
a word, especially a modifier, that indicates the quantity of something.

Origin:
1875–80; quantify + -er1

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World English Dictionary
 quantifier (ˈkwɒntɪˌfaɪə) —n 1. logic a.  a symbol including a variable that indicates the degree of generality of the expression in which that variable occurs, as (∃x) in (∃x)Fx, rendered "something is an F", (x) in (x)(Fx→Gx), rendered "all Fs are Gs" b.  any other symbol with an analogous interpretation: the existential quantifier, (∃x), corresponds to the words "there is something, x, such that …" 2. grammar a word or phrase in a natural language having this role, such as some, all, or many in English

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Computing Dictionary

### quantifier definition

logic
An operator in predicate logic specifying for which values of a variable a formula is true. Universally quantified means "for all values" (written with an inverted A, LaTeX \forall) and existentially quantified means "there exists some value" (written with a reversed E, LaTeX \exists). To be unambiguous, the set to which the values of the variable belong should be specified, though this is often omitted when it is clear from the context (the "universe of discourse"). E.g.
Forall x . P(x) not (Exists x . not P(x))
meaning that any x (in some unspecified set) has property P which is equivalent to saying that there does not exist any x which does not have the property.
If a variable is not quantified then it is a free variable. In logic programming this usually means that it is actually universally quantified.