Left downward monotonicity

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Left downward monotonicity is 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.


Utrecht Lexicon of Linguistics


  • 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.