Belief revision in institutions: a relaxation-based approach
Marc Aiguier, Jamal Atif, C. Hudelot, Isabelle Bloch · HAL (Le Centre pour la Communication Scientifique Directe) · 2015
Belief revision of knowledge bases represented by a set of sentences in a givenlogic has been extensively studied but for specific logics, mainly propositional,but also recently Horn and description logics. Here, we propose to generalize thisoperation from a model-theoretic point of view, by defining revision in a categoricalabstract model theory known under the name of theory of institutions. In thisframework, we generalize to any institution the characterization of the well knownAGM postulates given by Katsuno and Mendelzon for propositional logic in termsof minimal change with respect to an ordering among interpretations. Moreover,we study how to define revision, satisfying the AGM postulates, from relaxationnotions that have been first introduced in description logics to define dissimilaritymeasures between concepts, and the consequence of which is to relax the set ofmodels of the old belief until it becomes consistent with the new pieces of knowledge.The proposed general framework can be instantiated in different logics suchas propositional, description and Horn logics.