Difference between revisions of "Upward monotonicity"
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| + | ==Definition== | ||
'''Upward monotonicity''' is a property of [[determiner]]s and [[quantifier]]s in [[Generalized Quantifier]] Theory. A determiner D is left upward monotone (or ''left monotone increasing'' or persistent), if D(A,B) implies D(A',B) where A' is a superset of A. It is right upward monotone (or ''right monotone increasing'') if D(A,B) implies D(A,B'), where B subset B'. | '''Upward monotonicity''' is a property of [[determiner]]s and [[quantifier]]s in [[Generalized Quantifier]] Theory. A determiner D is left upward monotone (or ''left monotone increasing'' or persistent), if D(A,B) implies D(A',B) where A' is a superset of A. It is right upward monotone (or ''right monotone increasing'') if D(A,B) implies D(A,B'), where B subset B'. | ||
| − | + | == Example == | |
| − | + | The D ''some'' is left upward monotone and right upward monotone; see the validity of the implications in (i) and (ii) respectively: | |
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(i) If some dogs walked, then some animals walked. | (i) If some dogs walked, then some animals walked. | ||
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Because the interpretations of CN' and VP' are extensions of the interpretations of CN and VP respectively, the corresponding determiner or NP is also called closed under extension. | Because the interpretations of CN' and VP' are extensions of the interpretations of CN and VP respectively, the corresponding determiner or NP is also called closed under extension. | ||
| − | + | == Links == | |
| − | + | *[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Upward+monotonicity&lemmacode=137 Utrecht Lexicon of Linguistics] | |
| − | [http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Upward+monotonicity&lemmacode=137 Utrecht Lexicon of Linguistics] | ||
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| − | == | + | ==See also== |
| + | *[[left upward monotonicity]] | ||
| + | *[[right upward monotonicity]] | ||
| + | == 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. | ||
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[[Category:Semantics]] | [[Category:Semantics]] | ||
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Latest revision as of 16:55, 24 August 2014
Definition
Upward monotonicity is a property of determiners and quantifiers in Generalized Quantifier Theory. A determiner D is left upward monotone (or left monotone increasing or persistent), if D(A,B) implies D(A',B) where A' is a superset of A. It is right upward monotone (or right monotone increasing) if D(A,B) implies D(A,B'), where B subset B'.
Example
The D some is left upward monotone and right upward monotone; see the validity of the implications in (i) and (ii) respectively:
(i) If some dogs walked, then some animals walked. (ii) If some dogs walked rapidly, then some dogs walked.
Because the interpretations of CN' and VP' are extensions of the interpretations of CN and VP respectively, the corresponding determiner or NP is also called closed under extension.
Links
See also
References
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.
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