Merging Knowledge Bases in Possibilistic Logic by Lexicographic Aggregation

Belief merging is an important but difficult problem in Artificial Intelligence, especially when sources of information are pervaded with uncertainty. Many merging operators have been proposed to deal with this problem in possibilistic logic, a weighted logic which is powerful for handling inconsistency and deal- ing with uncertainty. They often result in a possibilistic knowledge base which is a set of weighted formulas. Although possibilistic logic is inconsistency tolerant, it suers from the well-known "drowning effect". Therefore, we may still want to obtain a consistent possi- bilistic knowledge base as the result of merg- ing. In such a case, we argue that it is not always necessary to keep weighted informa- tion after merging. In this paper, we define a merging operator that maps a set of pos- sibilistic knowledge bases and a formula rep- resenting the integrity constraints to a clas- sical knowledge base by using lexicographic ordering. We show that it satisfies nine pos- tulates that generalize basic postulates for propositional merging given in [11]. These postulates capture the principle of minimal change in some sense. We then provide an algorithm for generating the resulting knowl- edge base of our merging operator. Finally, we discuss the compatibility of our merging operator with propositional merging and es- tablish the advantage of our merging opera- tor over existing semantic merging operators in the propositional case.