quantifier
An operator in mathematics and 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. 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}.