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

Efficient representation and effective reasoning for multi-agent systems

In multi-agent systems, interactions between agents are often related to cooperation or competition in such a fashion that they can fulfil their tasks. Successful interactions often require agents to share common and unified knowledge about their working environment. However, autonomous agents observe and judge their surroundings by their own view. Consequently, agents possibly have partial and sometimes conflicting descriptions of the world. In scenarios where they have to coordinate, they are required to identify the shared knowledge in the group and to be able to reason with available information. This problem requires more sophisticated modelling and reasoning methods, which is beyond the classical logics and monotonic reasoning. We introduce a formal framework based on Defeasible Logic (DL) to describe the knowledge commonly shared by agents, and that obtained from other agents. This enables an agent to efficiently reason about the environment and intentions of other agents given available information. We propose to extend the reasoning mechanism of DL with the superior knowledge. This mechanism allows an agent to integrate its mental attitude with a more trustworthy source of information such as the knowledge shared by the majority of other agents

An Analysis of Sum-Based Incommensurable Belief Base Merging

International audienceDifferent methods have been proposed for merging multiple and potentially conflicting informations. Sum-based operators offer a natural method for merging commensurable prioritized belief bases. Their popularity is due to the fact that they satisfy the majority property and they adopt a non cautious attitude in deriving plausible conclusions. This paper analyses the sum-based merging operator when sources to merge are incommensurable, namely they do not share the same meaning of uncertainty scales. We first show that the obtained merging operator can be equivalently characterized either in terms of an infinite set of compatible scales, or by a well-known Pareto ordering on a set of models. We then study different families of compatible scales useful for merging process. This paper also provides a postulates-based analysis of our merging operators

Agents adapt to majority behaviours

Agents within a group can have different perceptions of their working environment and autonomously fulfil their goals. However, they can be aware of beliefs and goals of the group as well as other members so that they can adjust their behaviours accordingly. To model these agents, we explicitly include knowledge commonly shared by the group and that obtained from other agents. By avoiding actions which violate ``mental attitudes'' shared by the majority of the group, agents demonstrate their social commitment to the group. Defeasible logic is chosen as our representation formalism for its computational efficiency, and for its ability to handle incomplete and conflicting information. Hence, our agents can enjoy the low computational cost while performing ``reasoning about others''. Finally, we present the implementation of our multi-agent system

Analyse du comportement d'opérateurs de fusion basés sur la somme : du cadre commensurable au cadre incommensurable

National audienceDifferent methods have been proposed in the literature for merging multiple and potentially conflicting informations. Sum-based operators offer a natural method for merging commensurable prioritized belief bases. Their popularity is due to the fact that they satisfy the majority property and they adopt a non cautious attitude in deriving plausible conclusions. This paper analyses the sum-based merging operator when sources to merge are incommensurable, namely they do not share the same meaning of uncertainty scales. We first show that the obtained merging operator can be equivalently characterized either in terms of an infinite set of compatible scales, or by a well-known Pareto ordering on a set of models. We then study different families of compatible scales useful for merging process. This paper also provides a postulates-based analysis of our merging operators

Defeasible Logic to Model n-person Argumentation Game

In multi-agent systems, an individual agent can pursue its own goals, which may conflict with those hold by other agents. To settle on a common goal for the group of agents, the argumentation/dialogue game provides a robust and flexible tool where an agent can send its explanation for its goal in order to convince other agents. In the setting that the number of agents is greater than two and they are equally trustful, it is not clear how to extend existing argumentation/dialogue frameworks to tackle conflicts from many agents. We propose to use the defeasible logic to model the n-person argumentation game and to use the majority rule as an additional preference mechanism to tackle conflicts between arguments from individual agents

Fusion majoritaire de bases de croyances ordonnées sans commensurabilité des échelles de référence

International audienceLa fusion de croyances provenant de différentes sources potentiellement contradictoires est un domaine de recherche qui a été très étudié ces dernières années. Cependant, les méthodes de fusion actuellement proposées se basent sur l'hypothèse implicite suivante : les échelles de référence des différentes sources doivent être commensurables. Or cette hypothèse peut se révéler beaucoup trop forte si l'on considère des sources réellement hétérogènes. Nous proposons dans cet article d'adapter un opérateur de fusion majoritaire afin de traiter la fusion des bases de croyances supposées incommensurables. Pour cela, nous nous basons sur le concept d'échelles compatibles et nous montrons que cet opérateur est équivalent à un critère de Pareto. Enfin nous montrons comment le fait de considérer un ensemble fini d'échelles compatibles permet à cet opérateur de respecter le postulat de majorité

Une approche syntaxique pour le problème de la fusion de réseaux de contraintes qualitatives

National audienceDans cet article, nous nous intéressons au problème de la fusion de réseaux de contraintes qualitatives (RCQ) représentant des croyances ou des préférences locales sur les positions relatives d'entités spatiales ou temporelles. Nous définissons deux classes d'opérateurs de fusion d1 et d2 qui, à un ensemble de RCQ définis sur le même formalisme qualitatif et le même ensemble d'entités, associent un ensemble cohérent de configurations qualitatives représentant une vision globale de ces RCQ. Ces opérateurs sont paramétrés par une distance entre relations du formalisme qualitatif considéré et par des fonctions d'agrégation. Contrairement aux précédents opérateurs proposées pour la fusion de RCQ, nous optons pour une approche syntaxique, où chacune des contraintes des RCQ fournis a une influence sur le résultat de la fusion. Nous étudions les propriétés logiques des opérateurs de fusion définis et montrons leur équivalence sous certaines restrictions. Nous montrons que le résultat fourni par l'opérateur d2 correspond à l'ensemble des solutions optimales d'un RCQ pondéré particulier. Afin de calculer ces solutions, un algorithme basé sur la méthode de fermeture par faible composition étendu au cas des RCQ pondérés est proposé