Y. Gil et al. (Eds.): ISWC 2005, LNCS 3729, pp. 216 – 231, 2005. © Springer-Verlag Berlin Heidelberg 2005 On Applying the AGM Theory to DLs and OWL Giorgos Flouris, Dimitris Plexousakis, and Grigoris Antoniou Institute of Computer Science, FO.R.T.H. P.O. Box 1385, GR 71110, Heraklion, Greece {fgeo, dp, antoniou}@ics.forth.gr Abstract. It is generally acknowledged that any Knowledge Base (KB) should be able to adapt itself to new information received. This problem has been ex- tensively studied in the field of belief change, the dominating approach being the AGM theory. This theory set the standard for determining the rationality of a given belief change mechanism but was placed in a certain context which makes it inapplicable to logics used in the Semantic Web, such as Description Logics (DLs) and OWL. We believe the Semantic Web community would benefit from the application of the AGM theory to such logics. This paper is a preliminary study towards the feasibility of this application. Our approach raises interesting theoretical challenges and has an important practical impact too, given the central role that DLs and OWL play in the Semantic Web. 1 Introduction One of the crucial tasks towards the realization of the vision of the Semantic Web is the encoding of human knowledge in special structures (ontologies), using certain formal encodings (representation languages), such as DLs [3] and OWL [5]. Simply encoding the knowledge is not enough though; knowledge needs to be updated as well. There are several reasons for that: a piece of knowledge that was previously un- known, classified or otherwise unavailable may have become known; or a mistake may have occurred in the conceptualization of the domain or during the input; or the domain itself may have changed. In all these cases the ontology needs to be updated to accommodate the change. Even the development of an ontology is a highly itera- tive revision process, in which the ontology passes through several revising steps be- fore reaching its “final” version. For all the above reasons, developing an automatic, consistent and rational updat- ing method for ontologies is a task of great interest to the Semantic Web community. Despite this fact, the problem of ontology updating has been generally disregarded in the relevant literature [13]. In the current paper, we view this problem as a special case of the general problem of belief change (also known as belief revision) [8], which deals with the updating of a KB in the face of new information. The problem of belief change has been extensively studied in the literature, result- ing in several interesting results, the most important approach being the work by Al- chourron, Gärdenfors and Makinson (AGM for short) in [1], known as the AGM the- ory. In that paper, the authors did not attempt to introduce a new algorithm for belief change; instead, they proposed certain rationality constraints (known as the AGM pos- tulates) which should be satisfied by any rational belief change algorithm, thus setting