2015/02/08 by Marc Aiguier, Aiguier, Marc, Jamal Atif +5
Computer Science · #Advanced Algebra and Logic #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Logic, Reasoning, and Knowledge #Semantic Web and Ontologies
paper · pdf · doi:10.48550/arxiv.1502.02298
openalex publication_date 2015/02/08 · openalex created_date 2022/08/23 · openalex updated_date 2026/07/28
Belief revision of knowledge bases represented by a set of sentences in a\ngiven logic has been extensively studied but for specific logics, mainly\npropositional, and also recently Horn and description logics. Here, we propose\nto generalize this operation from a model-theoretic point of view, by defining\nrevision in an abstract model theory known under the name of satisfaction\nsystems. In this framework, we generalize to any satisfaction systems the\ncharacterization of the well known AGM postulates given by Katsuno and\nMendelzon for propositional logic in terms of minimal change among\ninterpretations. Moreover, we study how to define revision, satisfying the AGM\npostulates, from relaxation notions that have been first introduced in\ndescription logics to define dissimilarity measures between concepts, and the\nconsequence of which is to relax the set of models of the old belief until it\nbecomes consistent with the new pieces of knowledge. We show how the proposed\ngeneral framework can be instantiated in different logics such as\npropositional, first-order, description and Horn logics. In particular for\ndescription logics, we introduce several concrete relaxation operators tailored\nfor the description logic ALC and its fragments EL and ELext,\ndiscuss their properties and provide some illustrative examples.\n