Model-based belief merging without distance measures

Abstract

Merging operators try to define the beliefs of a group of agents according to the beliefs of each member of the group. Several model-based propositional belief merging operators have been proposed which use distance measures and aggregation functions. This paper introduces the notion of Partial Satisfiability which is an alternative way of measuring the satisfaction of a formula since this notion lets us have satisfaction values in the interval [0,1]. Partial Satisfiability allows us to define model-based merging operator. The proposal produces similar results to other merging approaches, but while other approaches require many merging operators in order to achieve satisfactory results for different scenarios this proposal obtains similar results for all these different scenarios with a unique operator. Moreover, unlike most of model-based approaches, this approach considers the case where the belief bases are inconsistent. The framework presented is in a preliminary state and further analysis of its properties is needed in order to characterize the proposed merging operator in terms of postulates.