Right upward monotonicity

Definition
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         =&gt;  all dogs walked (iv) At most two dogs walked rapidly =/=&gt; 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.

Links

 * Utrecht Lexicon of Linguistics