Belief merging within fragments of propositional logic

Recently, belief change within the framework of fragments of propositional logic has gained increasing attention. Previous works focused on belief contraction and belief revision on the Horn fragment. However, the problem of belief merging within fragments of propositional logic has been neglected so far. This paper presents a general approach to define new merging operators derived from existing ones such that the result of merging remains in the fragment under consideration. Our approach is not limited to the case of Horn fragment but applicable to any fragment of propositional logic characterized by a closure property on the sets of models of its formulae. We study the logical properties of the proposed operators in terms of satisfaction of merging postulates, considering in particular distance-based merging operators for Horn and Krom fragments.Comment: To appear in the Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014

The Incremental Satisfiability Problem for a Two Conjunctive Normal Form

We propose a novel method to review K ⊢ φ when K and φ are both in Conjunctive Normal Forms (CF). We extend our method to solve the incremental satisfiablity problem (ISAT), and we present different cases where ISAT can be solved in polynomial time. Especially, we present an algorithm for 2-ISAT. Our last algorithm allow us to establish an upper bound for the time-complexity of 2-ISAT, as well as to establish some tractable cases for the 2-ISAT problem

Révision des croyances dans une clôture propositionnelle de contraintes linéaires

National audienceRéviser des croyances par d'autres croyances consiste à modifier lespremières pour qu'elles soient cohérentes avec les secondes. Certainsopérateurs de révision de croyances s'appuient sur des distances entreinterprétations (qui servent à " mesurer " les modifications). Larévision des croyances a été étudiée dans plusieurs formalismes,notamment en logique propositionnelle et dans le formalisme desconjonctions de contraintes linéaires. Cet article étudie la révisiondans la clôture propositionnelle des contraintes linéaires, qui étendles deux formalismes précédents. La difficulté principale tient aufait qu'un opérateur s'appuyant sur une distance classique sur lesn-uplets de réels, telle que la distance de Manhattan, ne vérifierapas les postulats classiques de la révision. La solution proposée iciconsiste à utiliser une distance à ensemble de valeurs discret. Unopérateur de révision est ainsi décrit et étudié, et un algorithmepour cet opérateur est présenté, qui s'appuie sur une mise sous formenormale disjonctive et sur des optimisations linéaires

Belief revision within fragments of propositional logic

International audienc

Belief revision within fragments of propositional logic

International audienceBelief revision has been extensively studied in the framework of propositional logic, but just recently revision within fragments of propositional logic has gained attention. Hereby it is not only the belief set and the revision formula which are given within a certain language fragment, but also the result of the revision has to be located in the same fragment. So far, research in this direction has been mainly devoted to the Horn fragment of classical logic. Here we present a general approach to define new revision operators derived from known operators, such that the result of the revision remains in the fragment under consideration. Our approach is not limited to the Horn case but applicable to any fragment of propositional logic where the models of the formulas are closed under a Boolean function. Thus we are able to uniformly treat cases as dual Horn, Krom and affine formulas, as well