(quantifiers)

<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. See also first order logic. (2002-05-21)

In mathematics, a filter on a set X informally gives a notion of which subsets A \subseteq X are "large". Filter quantifiers are a type of logical quantifier which, informally, say whether or not a statement is true for "most" elements of X.

In the study of formal theories in mathematical logic, bounded quantifiers are often included in a formal language in addition to the standard quantifiers "∀" and "∃". Bounded quantifiers differ from "∀" and "∃" in that bounded quantifiers restrict the range of the quantified variable.

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.

A counting quantifier is a mathematical term for a quantifier of the form "there exists at least k elements that satisfy property X".

Quantifier elimination is a concept of simplification used in mathematical logic, model theory, and theoretical computer science. Informally, a quantified statement "\exists x such that \ldots" can be viewed as a question "When is there an x such that \ldots?

In logic, a quantifier is an operator that specifies how many individuals in the domain of discourse satisfy an open formula. For instance, the universal quantifier \forall in the first order formula \forall x P(x) expresses that everything in the domain satisfies the property denoted by P.

quantifier