quantifier

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)