Tailoring disjoint belief structures to the AGM framework
Theofanis I. Aravanis · Journal of Logic and Computation · 2024
Abstract The belief-structures model of Chopra and Parikh is perfectly suitable for representing the statics and dynamics of the beliefs of resource-bounded agents. Nevertheless, despite its favourable properties, it lies outside the AGM framework, the well-established paradigm for codifying rational belief revision of belief sets (i.e. logical theories), proposed by Alchourrón, Gärdenfors and Makinson. This feature can be attributed to two primary reasons: firstly, a multivalued logic is utilized for evaluating queries relative to a belief structure, and secondly, the objects under revision in the context of the belief-structures model are belief structures, rather than belief sets. Against this background, we present, in this article, a natural approach for adapting the revision of belief structures to an AGM-style revision while retaining the favourable properties of the belief-structures model. Under certain realistic assumptions, including the mutual disjointness of sublanguages of belief structures, a collection of interesting properties of the proposed method are identified, by investigating the satisfiability and violation of principal postulates of the belief-revision theory. Overall, it is demonstrated that the introduced approach constitutes a meaningful relevance-sensitive tool for integrating disjoint belief structures within the AGM framework, with potential applications in emerging fields such as digital twins, where precise and dynamic belief changes are essential for maintaining accurate simulations of real-world systems.