Quantifier (in predicate logic)
In predicate logic, the logical constant indicating whether a statement is universal or particular is calles quantifier. 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.
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.