Properties of Iterated Multiple Belief Revision

In this paper we investigate the properties of iterated multiple belief revision. We examine several typical assumptions for iterated revision operations with an ontology where an agent assigns ordinals to beliefs, representing strength or firmness of beliefs. A notion of minimal change is introduced to express the idea that if no evidence to show how a belief set should be reordered after it is revised, the changes on the ordering should be minimal. It has been shown that under the assumption of minimal change, the multiple version of Darwiche and Pearl’s postulate (C1) holds no matter in what degree new information is accepted. Moreover, under the same assumption, Boutilier’s postulate (CB) holds if and only if new information is always accepted in the lowest degree of firmness while Nayak et al.’s postulate (CN) holds if and only if new information is always accepted in the highest degree. These results provide an ontological base for analyzing the rationality of postulates of iterated belief revision.