http://glottopedia.org/index.php?action=history&feed=atom&title=Downward_monotonicityDownward monotonicity - Revision history2026-04-22T22:32:43ZRevision history for this page on the wikiMediaWiki 1.34.2http://glottopedia.org/index.php?title=Downward_monotonicity&diff=7531&oldid=prevWohlgemuth: utrecht2009-02-12T21:09:50Z<p>utrecht</p>
<p><b>New page</b></p><div>'''Downward monotonicity''' is a property of a [[determiner]] D(A,B). A determiner D can be downward monotone with respect to its left argument (A) or its right argument (B). It is ''left downward monotone'' (or left ''monotone decreasing'' or ''antipersistent'') if a true sentence of the form [<sub>S</sub> [<sub>NP</sub> D CN] VP] entails the truth of [<sub>S</sub> [<sub>NP</sub> D CN'] VP] where CN' denotes a subset of the set denoted by CN.<br />
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=== Example ===<br />
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the D ''at most two'' is left downward monotone:<br />
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(i) If at most two animals walked, then at most two dogs walked.<br />
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A determiner is ''right downward monotone'' (or ''right monotone decreasing'') if a true sentence of the form [<sub>S</sub> [<sub>NP</sub> D CN] VP] entails the truth of [<sub>S</sub> [<sub>NP</sub> D CN] VP'] where VP' denotes a subset of the set denoted by VP. EXAMPLE: the D ''at most two'' is also right downward monotone:<br />
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(ii) If at most two dogs walked, then at most two dogs walked in the garden.<br />
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If a determiner D is right downward monotone, then the [[generalized quantifier]] D(A) is often called ''downward monotone'' or ''monotone decreasing''. The opposite of downward monotonicity is [[upward monotonicity]].<br />
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=== Link ===<br />
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[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Downward+monotonicity&lemmacode=1098 Utrecht Lexicon of Linguistics]<br />
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=== References ===<br />
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* Barwise, J. &amp; R. Cooper 1981. ''Generalized Quantifiers and Natural Language,'' Linguistics and Philosophy 4, pp. 159-219<br />
* Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago.<br />
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[[Category:Semantics]]</div>Wohlgemuth