Traditional logic-based belief revision research focuses on designing rules to constrain the behavior of revision operators. Frameworks have been proposed to characterize iterated revision rules, but they are often too loose, leading to multiple revision operators that all satisfy the rules under the same belief condition. In many practical applications, such as safety critical ones, it is important to specify a definite revision operator to enable agents to iteratively revise their beliefs in a deterministic way. In this paper, we propose a novel framework for iterated belief revision by characterizing belief information through preference relations. Semantically, both beliefs and new evidence are represented as belief algebras, which provide a rich and expressive foundation for belief revision. Building on traditional revision rules, we introduce additional postulates for revision with belief algebra, including an upper-bound constraint on the outcomes of revision. We prove that the revision result is uniquely determined given the current belief state and new evidence. Furthermore, to make the framework more useful in practice, we develop a particular algorithm for performing the proposed revision process. We argue that this approach may offer a more predictable and principled method for belief revision, making it suitable for real-world applications.

In order to properly regulate iterated belief revision, Darwiche and Pearl (1997) model belief revision as revising epistemic states by propositions. An epistemic state in their sense consists of a belief set and a set of conditional beliefs. Although the denotation of an epistemic state can be indirectly captured by a total preorder on the set of worlds, it is unclear how to directly capture the structure in terms of the beliefs and conditional beliefs it contains. In this paper, we first provide an axiomatic characterisation for epistemic states by using nine rules about beliefs and conditional beliefs, and then argue that the last two rules are too strong and should be eliminated for characterising the belief state of an agent. We call a structure which satisfies the first seven rules a general epistemic state (GEP). To provide a semantical characterisation of GEPs, we introduce a mathematical structure called belief algebra, which is in essence a certain binary relation defined on the power set of worlds.We then establish a 1-1 correspondence between GEPs and belief algebras, and show that total preorders on worlds are special cases of belief algebras. Furthermore, using the notion of belief algebras, we extend the classical iterated belief revision rules of Darwiche and Pearl to our setting of general epistemic states.