View source for Right downward monotonicity

'''Right downward monotonicity''' is a particular semantic property of some [[NP]]s, interpreted as [[generalized quantifier]]s Q. Q has the property of being right [[downward monotonicity|downward monotone]] if and only if in a domain of entities E condition (i) holds.

 (i) for all X,Y subset E: if X in Q, and Y subset X, then Y in Q

Right downward monotonicity can be tested as in (ii): ''not every'' N is right downward monotone, ''every'' N is not.

 (ii) Not every dog walks =&gt;  not every dog walks rapidly
      Every dog walks    =/=&gt; every dog walks rapidly

So, a true sentence of the form [<sub>S</sub> NP VP] with a right downward monotone NP entails the truth of [<sub>S</sub> NP VP'], where the interpretation of VP' is a subset of the interpretation of VP. Right downward monotonicity can also be defined for determiners.

=== Links ===

[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Right+downward+monotonicity&lemmacode=348 Utrecht Lexicon of Linguistics]

=== References ===

* Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago.

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[[Category:Semantics]]

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