🤖 AI Summary
This work addresses the absence of a unified semantic framework for belief change that is independent of logical syntax, which has hindered systematic integration of classical and non-prioritized models. The paper proposes an abstract possible-world semantics (AWS) grounded in set theory, taking possible worlds as primitive elements and drawing on Grove’s sphere systems to define purely semantic operators for contraction and revision. This framework provides, for the first time, a logic-language-free unification of AGM, KM, and multiple belief change models. It not only simplifies and generalizes existing theories but also offers an isomorphic account of various belief change operations within propositional logic, thereby achieving a systematic and generalized foundation for belief set dynamics.
📝 Abstract
This article proposes a set-theoretic framework for belief change, called Abstract Worlds Semantics, in which no logical syntax is assumed. Inspired by Grove's (1988) results, our approach treats worlds as primitive elements, over which world contraction and world revision operators are defined. This semantic framework enables a unified analysis of belief change models. Within this framework, we unify classical and non-prioritized belief change constructions by defining versatile operators. When classical propositional logic is considered, our framework provides a homogeneous account of AGM, KM, and Multiple Change models. In summary, AWS systematizes belief change frameworks and operators, simplifying and generalizing belief change theory over belief sets.