A Description Logic for Vague Knowledge
C. Tresp, Ralf Molitor · 1998
This work introduces the concept language ALCF M which is an extension of ALC to many-valued logics.ALCF M allows to express vague concepts, e.g. more or less enlarged or very small.To realize this extension to many-valued logics, the classical notions of satis ability and subsumption had to be modi ed appropriately.For example, ALCF M -concepts are no longer either satis able or unsatis able, but they are satis able to a certain degree.The main contribution of this paper is a sound and complete method for computing the degree of subsumption between two ALCF M -concepts. IntroductionThis work takes its motivation from the occurrence of vague concept descriptions in dierent application areas.Often, application{inherent information is characterized by a very high degree of vagueness.Appropriate information systems must be able to process this kind of data.So far, there are no systems that really solve the corresponding problems due to the lack of powerful basic methods.A comfortable base of an information system can be obtained by a terminological knowledge representation system (TKRS), originated by Brachman and Schmolze in [2].The underlying knowledge representation formalism provides the user with a concept language to formulate and to solve application{relevant problems.Especially the advantage of symbolic representation allows the transparent acquisition and processing of information.But TKRS mostly lack the possibility to represent vague concept de nitions in an appropriate manner.Current approaches like [8,7,6] most often incorporate uncertainty calculus into the formalism of the TKRS.Uncertainty calculi deal with assumptions based on previous observations.These assumptions lack the feature of de nitive evidence and thus they must not be complete.The appearance of vagueness addresses a dierent problem (see [3]).Though the information is complete vagueness arises from the existence of knowledge areas with concepts that have no clear demarcation among others.The borderline between the de nitions of these concepts is rather hazy.For example, a medical statement that connects