Propositional belief base merging or how to merge beliefs/goals coming from several sources and some links with social choice theory

We give in this paper new results on merging operators. Those operators aim to define the goals (or beliefs) of an agents' group after the individuals' goals (beliefs). Using the logical framework of Konieczny and Pino Pérez [Proceedings of the Fifth European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU'99), Lecture Notes in Artificial Intelligence 1638, 1999, pp. 233-244] we study the relationships between two important sub-families of merging operators: majority operators and arbitration operators. An open question was to know if those two families were disjoint or not. We show that there are operators that belong simultaneously to the two families. Furthermore, the new family introduced allows the user to choose the “consensual level” he wants for his majority operator. We show at the end of this work some relationships between logical belief merging operators and social choice rules.