Left downward monotonicity
(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.
- Barwise, J. & R. Cooper 1981. Generalized Quantifiers and Natural Language, Linguistics and Philosophy 4, pp. 159-219
- Gamut, L.T.F. 1991. Logic, language, and meaning, Univ. of Chicago Press, Chicago.