Right downward monotonicity

Definition
Right downward monotonicity is a particular semantic property of some NPs, interpreted as generalized quantifiers Q. Q has the property of being right 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 [S NP VP] with a right downward monotone NP entails the truth of [S 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

 * Utrecht Lexicon of Linguistics