monotone (n.)

A term used in GENERALIZED QUANTIFIER THEORY to refer to a SEMANTIC property of NOUN PHRASES. A noun phrase is considered to be monotone increasing if, whenever a set is in its DENOTATION, all its supersets will also be in its denotation. This has the effect that a sentence containing the noun phrase as SUBJECT will systematically ENTAIL all sentences obtained by replacing the VERB PHRASE with a HYPERNYM. For example, Every dog is monotone increasing, so the sentence Every dog walks entails Every dog moves. The reverse pattern is observed with monotone decreasing noun phrases: No dog is monotone decreasing, so No dog moves entails No dog walks. This terminology is sometimes extended to DETERMINERS, in which case the terms left monotone increasing/decreasing and right monotone increasing/decreasing are used to distinguish monotonicity properties based on the determiner’s common noun and verb phrase arguments, respectively.