universal quantifier

universal quantifier
    n 1: a logical quantifier of a proposition that asserts that the
         proposition is true for all members of a class of things
    

quantifier
existential quantifier
universal 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)