Belief Contraction in Dynamic Epistemic Logic

2026-06-30

AI Summary

This work addresses the limitations of existing dynamic epistemic logics in adequately modeling belief contraction, particularly when dealing with failures of positive introspection and ambiguous public announcements. The paper introduces a direct mechanism for belief contraction within standard Kripke models, avoiding the need for plausibility orderings or additional constraints on doxastic accessibility relations. By extending the language and semantics of dynamic epistemic logic and integrating reduction axioms with model-transforming techniques, the authors develop a formal framework that supports belief contraction under private and semi-private announcements. The resulting system satisfies several classical contraction properties, precisely characterizes conditions under which contraction fails, and provides a sound and complete axiomatization for a generalized logic, thereby significantly enhancing the modeling of non-ideal belief revision.

Abstract

Dynamic epistemic logic represents belief change via model transformations induced by epistemic events. Its standard formulation (Baltag, Moss, Solecki, 1998) provides a natural account of belief expansion through the elimination of possibilities, but it cannot model belief contraction about factual propositions. A classic response enriches Kripke models with plausibility orderings, representing contraction as an update that promotes certain possibilities over others. We show that this approach has expressive limitations. In particular, the approach cannot model belief that violates positive introspection and contraction dynamics in response to a hedged public announcement that phi might be false. Motivated by these considerations, we introduce a mechanism for belief contraction defined directly on standard Kripke models, without any constraints on the doxastic accessibility relation. We show that it satisfies some of the standard properties of belief contraction but not others, study the conditions under which contraction may be unsuccessful, and provide a sound and complete axiomatization of the logic via reduction axioms. We also define a more general dynamic logic that is an extension of standard DEL and accommodates belief contractions due to events such as private or semi-private announcements, and provide a complete and sound axiomatization of the general logic.

Problem

• belief contraction
• dynamic epistemic logic
• Kripke models
• plausibility orderings
• positive introspection

Innovation

• belief contraction
• dynamic epistemic logic
• Kripke models
• reduction axioms
• doxastic accessibility