A Framework for Reasoning Precisely with Vague Concepts

Many knowledge-based systems need to represent vague concepts such as \old" and \tall". The practical approach of representing vague concepts as precise intervals over numbers (e.g., \old" as the interval [70,110]) is well-accepted in Arti cial Intelligence. However, there have been no systematic procedures, only ad hoc methods, to delimit the boundaries of intervals representing the vague predicates. A key observation is that the vague concepts and their interval boundaries are constrained by the underlying domain knowledge. Therefore, any systematic approach to assigning interval boundaries must take the domain knowledge into account. In this dissertation, we introduce a framework to represent the domain knowledge and use it to reason about the interval boundaries via a query language. This framework is comprised of a constraint language to represent logical constraints on the vague concepts, as well as numerical constraints on the interval boundaries; a query language to request information about the interval boundaries; and an algorithm to answer the queries. The algorithm preprocesses the constraints by extracting the numerical information from the logical constraints and then combines them with the given numerical constraints. We have implemented the framework and applied it to two domains to illustrate its usefulness.