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Monotonicity

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