On Applying the AGM Theory to DLs and OWL

Abstract

Abstract. It is generally acknowledged that any Knowledge Base (KB) should be able to adapt itself to new information received. This problem has been extensively 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.

Knowledge Base Revision in Description Logics

“…When defining his revision operator, he presumed that the terminological knowledge is more relevant than the assertional knowledge. Recently, some work has been done to analyze the feasibility of applying AGM theory on belief change to DLs [16,7,8]. However, none of them considers the explicit construction of a revision operator.…”

“…Furthermore, they did not consider the application of AGM postulates for revision in DLs where knowledge bases instead of knowledge sets are considered. The work in [16,8] is based on the coherence model, i.e. both the original and the revised knowledge bases should be knowledge sets which are knowledge bases closed under logical consequence.…”

“…There are various forms of inconsistencies, such as structural inconsistency, logical inconsistency and user-defined inconsistency. Among them, logical inconsistency in ontology evolution has attached lots of attention in recent years, where ontologies are represented by logical theories, such as description logics [21,1,8,11,10,14,19,25].…”

“…The application of AGM' theory to description logics is not trivial because it is based on the assumptions that generally fail for DLs [7]. For example, a DL is not necessarily closed under the usual operators such as ¬ and ∧ [8]. In [7,8], the basic AGM postulates for contraction were generalized to DLs and the feasibility of applying the generalized AGM theory of contraction to DLs and OWL was studied.…”

“…For example, a DL is not necessarily closed under the usual operators such as ¬ and ∧ [8]. In [7,8], the basic AGM postulates for contraction were generalized to DLs and the feasibility of applying the generalized AGM theory of contraction to DLs and OWL was studied. However, no explicit belief change operators were proposed in their papers.…”