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

Datalog± Ontology Consolidation

Knowledge bases in the form of ontologies are receiving increasing attention as they allow to clearly represent both the available knowledge, which includes the knowledge in itself and the constraints imposed to it by the domain or the users. In particular, Datalog ± ontologies are attractive because of their property of decidability and the possibility of dealing with the massive amounts of data in real world environments; however, as it is the case with many other ontological languages, their application in collaborative environments often lead to inconsistency related issues. In this paper we introduce the notion of incoherence regarding Datalog± ontologies, in terms of satisfiability of sets of constraints, and show how under specific conditions incoherence leads to inconsistent Datalog ± ontologies. The main contribution of this work is a novel approach to restore both consistency and coherence in Datalog± ontologies. The proposed approach is based on kernel contraction and restoration is performed by the application of incision functions that select formulas to delete. Nevertheless, instead of working over minimal incoherent/inconsistent sets encountered in the ontologies, our operators produce incisions over non-minimal structures called clusters. We present a construction for consolidation operators, along with the properties expected to be satisfied by them. Finally, we establish the relation between the construction and the properties by means of a representation theorem. Although this proposal is presented for Datalog± ontologies consolidation, these operators can be applied to other types of ontological languages, such as Description Logics, making them apt to be used in collaborative environments like the Semantic Web.Fil: Deagustini, Cristhian Ariel David. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Martinez, Maria Vanina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Falappa, Marcelo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Simari, Guillermo Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; Argentin

Conflict-Based Merging Operators

International audienceThis paper deals with propositional belief merging. The key problem in this setting is to define the beliefs/goals of a group of agents from a profile of bases, gathering the beliefs/goals of each member of the group. To this aim, a well-studied family of merging operators consists of distance-based ones: the models of the merged base are the closest interpretations to the given profile. Many operators from this family are based on the Hamming distance between interpretations, which can be viewed as a degree of conflict between them. In this paper, we introduce a more general family of merging operators, based on a more primitive concept, namely the conflict between interpretations itself. We show that this family of conflict-based merging operators includes many operators from the literature, both model-based ones and syntax-based ones. We present a number of comparison relations on conflict vectors characterizing operators from this family, and study the logical properties of conflict-based merging operators

Conflict-Based Merging Operators

International audienceThis paper deals with propositional belief merging. The key problem in this setting is to define the beliefs/goals of a group of agents from a profile of bases, gathering the beliefs/goals of each member of the group. To this aim, a well-studied family of merging operators consists of distance-based ones: the models of the merged base are the closest interpretations to the given profile. Many operators from this family are based on the Hamming distance between interpretations, which can be viewed as a degree of conflict between them. In this paper, we introduce a more general family of merging operators, based on a more primitive concept, namely the conflict between interpretations itself. We show that this family of conflict-based merging operators includes many operators from the literature, both model-based ones and syntax-based ones. We present a number of comparison relations on conflict vectors characterizing operators from this family, and study the logical properties of conflict-based merging operators