Monotonicity is a determiners (and quantifiers) can be classified according to their monotonicity-properties. A determiner D in a sentence of the form [S [NP D CN] VP] establishes a relation between the interpretations of CN and VP taken as sets of individuals. The monotonicity-properties of D can be found by extending or restricting the interpretations of CN and VP, and checking whether the resulting sentence is still true. Left upward/downward monotonicity deals with the extension/restriction of CN; right upward/downward monotonicity deals with the extension/restriction of VP. Left upward monotonicity is often called Persistence and left downward monotonicity Antipersistence; right monotonicity is then simply called monotonicity.
- 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.