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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
quantifier
existential quantifier
universal quantifier
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)