One axiomatic system for the ontology revision

Abstract

An ontology consists of concepts and the subsumption relation between these concepts, and is assumed to be a tree under the subsumption relation. In the process of building and maintaining ontologies, new statements which may contradict with exiting statements are added to the ontologies constantly. The ontology revision is necessary to accommodate new statements. In terms of the method of the axiomatization, one axiom system for the ontology revision, called the Z axiom system, is given, which is proved to satisfy the principles of the success, consistency and minimal change. Unlike the belief revision which is monotonic, the ontology revision may not be monotonic, and not only extracts some statements contradictory with a revising statement, extracts statements which are not contradictory with the revising statement, but also adds new statements to keep the tree structure of the revised ontology and satisfy the minimal change. One concrete ontology revision operator is proposed, which is proved to satisfy the Z axiom system.