# Restricted quantifier

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## Definition

**Restricted quantifier** is a quantifier which ranges over a subset of the universe of discourse selected by means of a predicate. Restricted quantification is sometimes represented as in (i), with the restricted quantifier between brackets and the predicate P indicating the subset:

(i) [ All(x) : P(x) ] Q(x) [ ThereIs(x) : P(x) ] Q(x)

It can also be represented in standard predicate logic by means of connectives:

(ii) All(x) [ P(x) -> Q(x) ] ThereIs(x) [ P(x) & Q(x) ]

In (ii) quantification is restricted to P: all or some entities that are P have property Q. In natural language, quantifiers are always restricted; either by the common noun following the quantifying determiner (*every man, some woman*) or by an inherent meaning element (*everyone, something*).

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## References

- Gamut, L.T.F. 1991.
*Logic, language, and meaning,*Univ. of Chicago Press, Chicago.