Belief Revision, Minimal Change and Relaxation: A General Framework based on Satisfaction Systems, and Applications to Description Logics

TL;DR

This paper introduces a general framework for belief revision based on satisfaction systems, extending AGM postulates and relaxation concepts to various logics including description logics, with practical operators for $ ext{ALC}$, $ ext{EL}$, and $ ext{EL}^{{ ext{ext}}}$.

Contribution

It generalizes belief revision to satisfaction systems and develops relaxation-based revision operators for description logics, broadening applicability beyond propositional logic.

Findings

Framework applicable to propositional, first-order, and description logics

Concrete relaxation operators for $ ext{ALC}$, $ ext{EL}$, and $ ext{EL}^{{ ext{ext}}}$

Illustrative examples demonstrating the operators' properties

Abstract

Belief revision of knowledge bases represented by a set of sentences in a given logic has been extensively studied but for specific logics, mainly propositional, and also recently Horn and description logics. Here, we propose to generalize this operation from a model-theoretic point of view, by defining revision in an abstract model theory known under the name of satisfaction systems. In this framework, we generalize to any satisfaction systems the characterization of the well known AGM postulates given by Katsuno and Mendelzon for propositional logic in terms of minimal change among interpretations. Moreover, we study how to define revision, satisfying the AGM postulates, from relaxation notions that have been first introduced in description logics to define dissimilarity measures between concepts, and the consequence of which is to relax the set of models of the old belief until it becomes consistent with the new pieces of knowledge. We show how the proposed general framework can be instantiated in different logics such as propositional, first-order, description and Horn logics. In particular for description logics, we introduce several concrete relaxation operators tailored for the description logic $\ALC{}$ and its fragments $\EL{}$ and $\ELext{}$, discuss their properties and provide some illustrative examples.