Difference between revisions of "Right upward monotonicity"
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+ | ==Definition== | ||
'''Right upward monotonicity''' is the property of an [[NP]], interpreted as a [[quantifier]] Q, which has the property of being right [[upward monotonicity|upward monotone]] if and only if for all subsets X and Y of the domain of entities E condition (i) holds. | '''Right upward monotonicity''' is the property of an [[NP]], interpreted as a [[quantifier]] Q, which has the property of being right [[upward monotonicity|upward monotone]] if and only if for all subsets X and Y of the domain of entities E condition (i) holds. | ||
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So a true sentence of the form [<sub>S</sub> NP VP] with a right upward monotone NP entails the truth of [<sub>S</sub> NP VP'], where the interpretation of VP' is a superset of the interpretation of VP. Right upward monotonicity can also be defined for determiners. | So a true sentence of the form [<sub>S</sub> NP VP] with a right upward monotone NP entails the truth of [<sub>S</sub> NP VP'], where the interpretation of VP' is a superset of the interpretation of VP. Right upward monotonicity can also be defined for determiners. | ||
− | + | == Links == | |
− | + | *[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Right+upward+monotonicity&lemmacode=352 Utrecht Lexicon of Linguistics] | |
− | [http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Right+upward+monotonicity&lemmacode=352 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. | ||
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[[Category:Semantics]] | [[Category:Semantics]] | ||
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Latest revision as of 18:28, 28 September 2014
Definition
Right upward monotonicity is the property of an NP, interpreted as a quantifier Q, which has the property of being right upward monotone if and only if for all subsets X and Y of the domain of entities E condition (i) holds.
(i) if X in Q and X subset Y, then Y in Q
Right upward monotonicity can be tested as in (ii): all N is right upward monotone, at most two N is not.
(ii) All dogs walked rapidly => all dogs walked (iv) At most two dogs walked rapidly =/=> at most two dogs walked
So a true sentence of the form [_{S} NP VP] with a right upward monotone NP entails the truth of [_{S} NP VP'], where the interpretation of VP' is a superset of the interpretation of VP. Right upward monotonicity can also be defined for determiners.
Links
References
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.
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