Weighted Merging of Propositional Belief Bases

In standard propositional belief merging, one implicit assumption is that all sources have exactly the same importance. But there are many situations where the sources have different importance/reliability/expertise that have to be taken into account in the merging process. In this work we study the problem of weighted merging operators, which aimed to take these weights into account in a sensible way. We give a syntactical characterization of these operators, and then we state a representation theorem in terms of plausibility preorders on interpretations. We also propose a general method to build weighted distance-based merging operators, and provide some concrete examples, using two different weight functions.