Updating Description Logics using the AGM Theory
Giorgos Flouris, Dimitris Plexousakis, Grigoris Antoniou · 2005
2 Preliminaries We consider the use of belief change techniques to address the problem of updating Knowledge Bases (KBs) based on Description Logics (DLs). We focus on the feasibility of the application of the AGM theory in DL KBs, evaluate the difficulties of the approach and determine the applicability of the method in certain families of DLs. For those DLs that are found compatible with the AGM model, we also describe a contraction operator that satisfies the AGM postulates. Finally, as an application of interest in the area of the Semantic Web, we study OWL, a W3C recommendation, and show that it is incompatible with the AGM model. 2.1 Description Logics The term Description Logics [Baader et al., 2002] refers to a family of knowledge representation languages, heavily used in the Semantic Web. The basic blocks that are used to represent knowledge in DLs are classes (representing concepts), roles (representing binary relationships between concepts) and individuals (representing individual objects). These are used to form more complex expressions (terms) using certain operators. Knowledge is represented using axioms; an axiom represents a certain relationship (such as inclusion, membership and others) between terms using certain connectives. The part of the DL KB dealing with concepts and roles is called the Tbox, while individuals are described in the Abox. The operators and connectives that a certain DL admits determine the type and complexity of the available axioms, which, in turn, determine the expressive power and the reasoning complexity of the DL.