Belief revision, minimal change and relaxation: A general framework based on satisfaction systems, and applications to description logics

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 modeltheoretic 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 ELU , discuss their properties and provide some illustrative examples.

Using Adaptive Logics for Expression of Context and Interoperability in DL Ontologies

“…AGM postulates do not directly apply to DL. In their work for generalizing AGM postulates so that they become applicable to DL and other non-classical logics, Aiguier et al [12] use relaxations to define revision operators satisfying weakened AGM postulates. The resulting theoretical framework is demonstrated with two DL: E L and E LU .…”

Explanatory relations in arbitrary logics based on satisfaction systems, cutting and retraction

“…We recall here the basic notions of satisfaction systems needed in this paper. The presentation follows the one in [1], where we give a more complete presentation of satisfaction systems, including the properties and their proofs, that are omitted here.…”

“…Here weaker properties are required for retraction, that allow defining a larger set of suitable operators for abduction for different logics. This approach is similar to the one proposed for revision in [1], where revision operators were defined from relaxation in satisfaction systems, and then instantiated in various logics. An important feature of the proposed explanations based on retraction is that generation and selection steps are merged, or at least the set of generated hypotheses is reduced, thus facilitating the selection step.…”

“…Several other retractions could be proposed. In particular, several relaxations proposed in [1] for revision could be modified to become retractions. For instance, relaxing C D can be performed either by retracting C or by relaxing D. Similarly, retracting C D could be performed either by relaxing C or by retracting D.…”

A Closeness- and Priority-Based Logical Study of Social Network Creation

“…2 Notions of similarity (in particular, when used for defining notions of distance) have been valuable for different logical frameworks. On the syntactic level, they have been used for knowledge bases 3 and belief revision (Alchourrón et al 1985;Aiguier et al 2018). On the semantic level, they have been used for representing information change, including methods for knowledge update (Baral and Zhang 2005), semantic forms of belief revision (Katsuno and Mendelzon 1992) and others (Bloch et al 2018).…”