Restricted quantifier

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) -&gt; Q(x) ] ThereIs(x) [ P(x) &amp; 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).

Links

 * Utrecht Lexicon of Linguistics