SEMANTICS: 1. (in predicate logic) the logical constant in predicate logic indicating whether a statement is universal or particular. The universal quantifier All indicates that all entities in the universe have a given property while the existential quantifier ThereIs indicates that at least one entity has the property:
(i) a All(x) [ P(x) ] "Every x has property P" b ThereIs(y) [ Q(y) ] "At least one y has property Q"The term quantifier can either be used for the symbols All and ThereIs themselves or for the combination with the variable they bind: All(x) and ThereIs(y). A more complex use of quantifiers is shown in (ii):
(ii) All(x) [ P(x) -> ThereIs(y) [ Q(y) & R(x,y) ]which might be the translation of a sentence like Every teenage girl adores a rock star.
|LIT.||Gamut, L.T.F. (1991)|