A synthetic view of belief revision with uncertain inputs in the framework of possibility theory

Abstract

This paper discusses belief revision under uncertain inputs in the framework of possibility theory. This framework is flexible enough to allow for numerical and ordinal revision procedures. It is emphasized that revision under uncertain inputs can be understood in two different ways, depending on whether the input is viewed as a constraint to be enforced, or as an unreliable piece of information. Two revision rules are proposed to implement these forms of revision. It is shown that M. A. Williams's transmutations, originally defined in the setting of Spohn's functions, can be captured in possibility theory, as well as Boutilier's natural revision. The use of conditioning greatly simplifies the description of these belief change operations. Lastly, preliminary results on implementing revision rules at the syntactic level are given. © 1997 Elsevier Science Inc.