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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.
2. (in Generalized Quantifier Theory) the model-theoretic interpretation of a noun phrase as a set of of sets.
LIT. Gamut, L.T.F. (1991)