Conditional Doxastic Models: A Qualitative Approach to Dynamic Belief Revision

Alexandru Baltag, Sonja Smets
2006 Electronical Notes in Theoretical Computer Science  
In this paper, we present a semantical approach to multi-agent belief revision and belief update. For this, we introduce relational structures called conditional doxastic models (CDM's, for short). We show this setting to be equivalent to an epistemic version of the classical AGM Belief Revision theory. We present a logic of conditional beliefs that is complete w.r.t. CDM's. Moving then to belief updates (sometimes called "dynamic" belief revision) induced by epistemic actions, we consider two
more » ... articular cases: public announcements and private announcements to subgroups of agents. We show how the standard semantics for these types of updates can be appropriately modified in order to apply it to CDM's, thus incorporating belief revision into our notion of update. We provide a complete axiomatization of the corresponding dynamic doxastic logics. As an application, we solve a "cheating version" of the Muddy Children Puzzle.
doi:10.1016/j.entcs.2006.05.034 fatcat:cjxhzwk7gfathgwgcgdowo52u4