A Theory of Vague Adjectives Grounded in Relevant Observables

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