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Belief revision of knowledge bases represented by a set of sentences in agiven logic has been extensively studied but for specific logics, mainlypropositional, and also recently Horn and description logics. Here, we proposeto generalize this operation from a model-theoretic point of view, by definingrevision in an abstract model theory known under the name of satisfactionsystems. In this framework, we generalize to any satisfaction systems thecharacterization of the well known AGM postulates given by Katsuno andMendelzon for propositional logic in terms of minimal change amonginterpretations. Moreover, we study how to define revision, satisfying the AGMpostulates, from relaxation notions that have been first introduced indescription logics to define dissimilarity measures between concepts, and theconsequence of which is to relax the set of models of the old belief until itbecomes consistent with the new pieces of knowledge. We show how the proposedgeneral framework can be instantiated in different logics such aspropositional, first-order, description and Horn logics. In particular fordescription logics, we introduce several concrete relaxation operators tailoredfor the description logic $\ALC{}$ and its fragments $\EL{}$ and $\ELext{}$,discuss their properties and provide some illustrative examples.

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