Journal of Semantics 2 (3-4):253-272 (1983)

Abstract
In its traditional interpretation, Frege's principle of compositionality is not sufficiently flexible to have a wide applicability to natural languages. In a fuzzy-set-theoretic setting which is outlined in this paper, Frege's principle is modified and broadened by allowing the meaning of a proposition, p, to be composed not from the meaning of the constituents of p, but, more generally, from the meaning of a collection of fuzzy relations which form a so-called explanatory database that is associated with p. More specifically, through the application of test-score: semantics, the meaning of p is represented as a procedure which tests, scores and aggregates the elastic constraints which are implicit in p. The employment of fuzzy sets in this semantics allows p to contain fuzzy predicates such as tall, kind, much richer, etc.; fuzzy quantifiers such as most, several, few, usually etc.; modifiers such as very, more or less, quite somewhat, etc.; and other types of semantic entities which cannot be dealt with within the framework of classical logic. The approach described in the paper suggests a way of representing the meaning of dispositions, e.g., Overeating causes obesity, Icy roads are slippery, Young men like young women, etc. Specifically, by viewing a disposition, d, as a proposition with implicit fuzzy quantifiers, the problem of representing the meaning of d may be decomposed into (a) restoring the suppressed fuzzy quantifiers and/or fuzzifying the nonfuzzy quantifiers in the body of d; and (b) representing the meaning of the resulting dispositional proposition through the use of test-score semantics. To place in evidence the logical structure of p and, at the same time, provide a high-level description of the composition process, p may be expressed in the canonical form “X is F” where X=(XI,…,Xn) is an explicit n-ary variable which is constrained by p, and F is a fuzzy n-ary relation which may be interpreted as an elastic constraint on X. This canonical form and the meaning-composition process for propositions and dispositions are illustrated by several examples among which is the proposition p≜ Over the past few years Naomi earned far more than most of her close friends
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DOI 10.1093/semant/2.3-4.253
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