A Fuzzy Description Logic.

In Proceedings of AAAI-98, 15th National Conference on Artificial Intelligence, pages 594--599, Madison, Wisconsin, 1998.

Description Logics (DLs, for short) allow reasoning about individuals and concepts, i.e. set
of individuals with common properties. Typically, DLs are limited to dealing with crisp, well
defined concepts. That is, concepts for which the problem whether an individual is an instance
of it is a yes/no question. More often than not, the concepts encountered in the real world do
not have a precisely defined criteria of membership: we may say that an
individual is an instance of a concept only to a certain degree, depending on the individual's
properties. Concepts of this kind are rather vague than precise. As fuzzy logic directly deals
with the notion of vagueness and imprecision, it offers an appealing foundation for a
generalisation of DLs to vague concepts.

In this paper we present a general fuzzy DL, which combines fuzzy logic with DLs. We
define its syntax, semantics and present constraint propagation calculi for reasoning in it.