Fuzzy Logic and Restricted Quantifiers

Abstract

This paper is part of an ongoing attempt to do justice to both a linguist’s concerns and a logician’s within a single consistent system. The principal respect in which a linguist’s concerns will affect what follows here is the matter of coverage: I will assume Lakoff’s (1972) conclusion that a multi-valued logic is essential for an adequate treatment of the semantics of a large amount of natural language vocabulary, particularly adjectives such as fat, obnoxious, and pleasant, which do not make a clear division between things of which they are true and things of which they are false, nouns such as vermin, vegetable, and toy, which denote categories with imprecise boundaries, and many ‘hedge’ words such as somewhat, quite, pretty much, and par excellence. I will take truth values to be real numbers on the interval from 0 to 1, with 0 corresponding to unqualified falsehood, 1 to unqualified truth, and intermediate numbers to intermediate degrees of truth to which such terms as ‘fairly true’, ‘pretty well false’, and the like could be applied¹.