Relaxation-based revision operators in description logics

Abstract: As ontologies and description logics (DLs) reach out to a broader audience, several reasoning services are developed in this context. Belief revision is one of them, of prime importance when knowledge is prone to change and inconsistency. In this paper we address both the generalization of the well-known AGM postulates, and the definition of concrete and well-founded revision operators in different DL families. We introduce a model-theoretic version of the AGM postulates with a general definition of inconsistency, hence enlarging their scope to a wide family of non-classical logics, in particular negation-free DL families. We propose a general framework for defining revision operators based on the notion of relaxation, introduced recently for defining dissimilarity measures between DL concepts. A revision operator in this framework amounts to relax the set of models of the old belief until it reaches the sets of models of the new piece of knowledge. We demonstrate that such a relaxation-based revision operator defines a faithful assignment and satisfies the generalized AGM postulates. Another important contribution concerns the definition of several concrete relaxation operators suited to the syntax of some DLs (ALC and its fragments EL and ELU).