Right downward monotonicity
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 => not every dog walks rapidly Every dog walks =/=> 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.
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.