The Algebra of Multi-Agent Dynamic Belief Revision

We refine our algebraic axiomatization in [8, 9] of epistemic actions and epistemic update (notions defined in [5, 6] using a relational, Kripke-style semantics), to incorporate a mechanism for dynamic belief revision in a multi-agent setting. Our approach has a number of novel features, when compared with traditional belief revision systems such as AGM [2]. Firstly: while traditional belief revision was dealing only (the revision of theories comprised of) ”facts”, we can also revise (theories comprised of) epistemic/doxastic propositions; thus, some of traditional AGM postulates have to be modified in order to deal with non-stable epistemic propositions, such as the ones generated by the so-called Moore sentences1. Secondly, ours is a dynamic belief revision, i.e. a particular form of update: an action q happens, changing the original theory m to a revised theory m ? q. Thirdly: this dynamic character is enhanced by the fact that we allow revision of actions, and not just of ”static” theories; the agent has theories about the current action, and these may be revised by further actions. Fourthly: we do multiagent belief revision. Our approach, though related in aim, is different in flavour from the work of [14] on Kripke-style belief revision and from the more recent work of [3, 15] on dynamic belief revision: while these approaches are semantic and ”quantitative” (being based on having ”degrees of belief” as the quantitative basis of belief revision), our approach is purely qualitative and axiomatic, being thus closer in spirit to the traditional AGM approach. Indeed, our aim is simply to find the ”correct” axiomatization of the dynamic (and multi-agent) version of AGM.