Modeling nonintersective adjectives using operator logics. (English) Zbl 1303.03063

Bankston, Paul

Rev. Mod. Log. 9 (2001/2003), No. 1-2, 9-28 (2003).

Summary: Our topic is one that involves the interface between natural language and mathematical logic. First-order predicate language/logic does a good job approximating many parts of (English) speech, i.e., nouns, verbs and prepositions, but fails decidedly when it comes to, say, adjectives. In particular, it cannot account for the quite different ways in which the adjectives green and big modify a noun such as chair. In the former case, we can easily view a world in which the class of green chairs is the intersection of the class of green things with the class of chair-things. By contrast, the way big modifies a noun depends on the noun itself: a big chair is microscopic when compared to the smallest of galaxies. We investigate logical languages inspired by this phenomenon; particularly those with variables ranging over individuals and with variable-binding operators akin to generalized quantifiers.

MSC:

03B65	Logic of natural languages
03C80	Logic with extra quantifiers and operators

Keywords:

adjectives in natural language; categorization problem; operator languages; constrained semantics; expressive power; completeness; compactness