Found:

downward monotonicity

**SEMANTICS: **a property of a **determiner** D(A,B). A determiner D can be downward monotone with respect to its left argument (A) or its right argument (B). It is *left downward monotone* (or left *monotone decreasing* or *antipersistent*) if a true sentence of the form [_{S} [_{NP} D CN] VP] entails the truth of [_{S} [_{NP} D CN'] VP] where CN' denotes a subset of the set denoted by CN.
** EXAMPLE:** the D *at most two* is left downward monotone:

(i) If at most two animals walked, then at most two dogs walked.A determiner is

(ii) If at most two dogs walked, then at most two dogs walked in the garden.If a determiner D is right downward monotone, then the

LIT. | Barwise, J. & R. Cooper (1981) Gamut, L.T.F. (1991) |