Difference between revisions of "Restricted quantifier"
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| − | + | ==Definition== | |
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'''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: | '''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: | ||
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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''). | 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 == | |
| − | + | *[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Restricted+quantifier&lemmacode=339 Utrecht Lexicon of Linguistics] | |
| − | [http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Restricted+quantifier&lemmacode=339 Utrecht Lexicon of Linguistics] | ||
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| + | == References == | ||
* Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago. | * Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago. | ||
{{dc}} | {{dc}} | ||
[[Category:Semantics]] | [[Category:Semantics]] | ||
Latest revision as of 17:32, 28 September 2014
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).
Links
References
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.
