Relaxation-based revision operators in description logics

TL;DR

This paper introduces a relaxation-based framework for belief revision in description logics, generalizing AGM postulates and defining concrete operators for various DL families to handle inconsistency and knowledge updates.

Contribution

It generalizes AGM postulates to non-classical logics and proposes a relaxation-based approach for belief revision in description logics, including concrete operators for specific DLs.

Findings

Relaxation-based revision operators satisfy generalized AGM postulates.

Framework applicable to negation-free and other non-classical DLs.

Concrete operators developed for ALC, EL, and ELU 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).