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.
