A Qualitative Theory of Dynamic Interactive Belief Revision

We present a logical setting that incorporates a belief-revision mechanism within Dynamic-Epistemic logic. As the “static” basis for belief revision, we use epistemic plausibility models, together with a modal language based on two epistemic operators: a “knowledge” modality K (the standard S5, fully introspective, notion), and a “safe belief” modality 2 (“weak”, non-negatively-introspective, notion, capturing a version of Lehrer’s “indefeasible knowledge”). To deal with “dynamic” belief revision, we introduce action plausibility models, representing various types of “doxastic events”. Action models “act” on state models via a modified update product operation: the “ActionPriority” Update. This is the natural dynamic generalization of AGM revision, giving priority to the incoming information (i.e. to “actions”) over prior beliefs. We completely axiomatize this logic, and show how our update mechanism can “simulate”, in a uniform manner, many different belief-revision policies.