Reconciling Diierent Semantics for Concept Deenition (extended Abstract)

Most of the modern formalisms used in Databases and Arti cial Intelligence for describing an application domain allow for using the notions of concept or class and relationship among con cepts There are basically two ways of using and describing classes In the rst one prescriptive approach the description formalism allows for expressing properties of the classes to be repre sented thus prescribing the properties that instances of the classes must possess In the second one de nitional approach the formalism allows for providing the de nition of a class i e a set of properties that precisely characterize the instances of the class While the prescriptive approach is quite well understood and established the de nitional approach is still the subject of an interesting debate regarding both its nature and its semantic foundation In particular it is well known that there are various possibilities for assigning a meaning to a de nition of a class especially if such a de nition contains some sort of recursion Baa Neb BB Bee In this paper we are concerned with the semantical problems related to the de nitional ap proach arguing that instead of choosing a single style of semantics for the knowledge represen tation formalism we achieve a better result by adopting a powerful formalism allowing di erent semantics to coexist Speci cally we present a concept language an extension of ALC with the above characteristics discuss its properties and describe a method for reasoning e ectively with knowledge bases T Boxes expressed in the language Such a method is based on a correspon dence with a particular modal logic of programs called modal mu calculus Koz ES SA which has been recently investigated for expressing temporal properties of reactive and parallel processes Sti Lar