Right upward monotonicity
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.
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.