A Logic for Iterated Belief Revision

Representing belief information is a fundamental problem in the field of belief revision. The AGM framework uses a deductively closed set of formulas, known as a theory, to represent the belief information of an agent, because the belief information of a rational agent should satisfy properties similar to a theory. However, in the iterated revision setting, the DP framework uses conditional beliefs like (φ | ψ) to represent such information, which is not natural, as conditional beliefs are not formulas and logical connections between them cannot be characterized clearly. In this paper, we propose a novel logic system for representing belief information under iterated revision as a theory in this logic system, which is more natural than the approach of the DP framework. We also prove the soundness and completeness of the logic system, such that it is readily usable for performing iterated revision. Finally, we showed that this logic system is powerful enough to represent general epistemic state as a theory, which is more general than the representation of the DP framework.