Left downward monotonicity
SEMANTICS: a property of a determiner D in Generalized Quantifier Theory. A determiner D is left downward monotone if and only if in a domain of entities E condition (i) holds.
(i) for all A, B, A' subset E: if D(A,B) and A' subset A, then D(A',B)Left downward monotonicity can be tested as in (ii); as shown there, all and no are left downward monotone, but some and exactly two are not.
(ii) a If all/no animals walked, then all/no dogs walked. b If some/exactly two animals walked, then some/exactly two dogs walked.Other terms are antipersistent and left monotone decreasing.
|LIT.||Barwise, J. & R. Cooper (1981)|
Gamut, L.T.F. (1991)