The ambiguity and vagueness of natural language vocabulary is one of the biggest obstacles to formalising reasoning systems that can operate with natural language concepts. The paper presents a formal theory of the logic of vague adjectives, which is based on two key ideas: 1) a sharp distinction between count noun concepts and adjectival concepts is build into both syntax and semantics; 2) valid inferences with vague adjectives are explained by means of a theory of the relevance of particular observables to the applicability of any given adjective. The theory is presented as a first-order formalism in which conceptual elements are combined by means of a small number of primitive logical predicates, which are axiomatised and given a set-theoretic semantics. The relationship of the proposed formalism to existing approaches using fuzzy logic or supervaluationistic modal semantics is also considered. A possible solution to the 'sorites'paradox is also outlined.
Subjects: 11. Knowledge Representation
Submitted: Mar 9, 2006