The Algebra of Multi-Agent Dynamic Belief Revision

We refine our algebraic axiomatization in [A. Baltag, B. Coecke, M. Sadrzadeh, Epistemic actions as resources in Proceedings of Logics for Resources Programs Processes (LRPP) workshop in LiCS 2004, http://www.er.uqam.ca/nobel/philmath/LicsWSPROC.pdf, A. Baltag, B. Coecke, M. Sadrzadeh, Algebra and Sequent Calculus for Epistemic Action', Electrical Notes in Computer Science 126 (2005) 27–52] of epistemic actions and epistemic update (notions defined in [A. Baltag, L.S. Moss, Logics for epistemic programs, Synthese 139 (2004) 165–224, A. Baltag, L.S. Moss, S. Solecki, The logic of public announcements, common knowledge and private suspicions, CWI Technical Report SEN-R9922, 1999] using Kripke-style semantics), to incorporate a mechanism for dynamic belief revision in a multi-agent setting. We encode revision as a particular form of epistemic update, as a result of which we can revise with epistemic propositions as well as facts, we can also revise theories about actions as well as about states of the worlds, and we can do multi-agent belief revision. We show how our setting can be applied to a cheating version of the muddy children puzzle where by using this logic, after the cheating happens, honest children will not get contradictory beliefs.