Reasoning Precisely with Vague Concepts

Abstract

Many knowledge-based systems need to represent vague concepts. Although the practical approach of representing vague concepts as precise intervals over numbers is well-accepted in AI, there is no systematic method to delimit the boundaries of intervals, only ad hoc methods. We present a framework to reason precisely with vague concepts based on the observation that the vague concepts and their interval-boundaries are constrained by the underlying domain knowledge. The framework is comprised of a constraint language to represent logical constraints on vague concepts, as well as numerical constraints on the intervalboundaries; a query language to request information about the interval boundaries; and a computational mechanism to answer the queries. A key step in answering queries is preprocessing the constraints by extracting the numerical constraints from the logical constraints and combining them with the given numerical constraints.