Revision with probability

This paper investigates belief revision with uncertainty. Normally, this kind of revision is processed in the framework of possibilistic logic, which is good at processing incomplete and imprecise information. However, the possibilistic logic based revision does not provide a probabilistic explanation for uncertainty. To solve this problem, it is necessary to express this problem from a perspective of probability. This paper proposes the definitions of formula probability and model probability, and then derives the conversion equation between them. To deal with uncertain belief revision, a probabilistic estimation is used. The approaches for revision with a reliable input and an uncertain input are discussed respectively. At last, differences between our approach and the existing ones for uncertain revision are explored.