On Definite Iterated Belief Revision with Belief Algebras

TL;DR

This paper introduces a new belief revision framework using belief algebras and preference relations, ensuring deterministic and predictable belief updates suitable for safety-critical applications.

Contribution

It proposes a novel semantic framework for iterated belief revision with belief algebras, establishing conditions for unique revision outcomes and providing a practical algorithm.

Findings

Revision results are uniquely determined by current beliefs and new evidence.

The framework ensures deterministic belief revision outcomes.

A practical algorithm for belief revision is developed.

Abstract

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.