An Abstract Worlds Semantic Framework for Belief Change Operators
2026-06-01 • Artificial Intelligence
Artificial Intelligence
AI summaryⓘ
The authors introduce a new way to look at how beliefs change, called Abstract Worlds Semantics, which doesn’t rely on any specific logical language. They build on previous work by treating possible worlds as basic building blocks and define rules for changing beliefs based on these worlds. Their framework brings together different belief change methods into one system and works well with classical logic too. Overall, their approach helps simplify and unify the study of how beliefs can logically be updated or revised.
belief changeAbstract Worlds Semanticspossible worldsworld contractionworld revisionAGM theoryKM modelsmultiple changenon-prioritized belief changepropositional logic
Authors
Daniel Grimaldi, M. Vanina Martinez, Ricardo O. Rodriguez
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.