Refinement Quantified Logics of Knowledge

Refinement quantifiers were introduced to quantify over all refinements of a model in modal logic, where a refinement is described by a simulation relation. Given the “possible worlds” interpretation of modal logic, a refinement corresponds to an agent ruling out certain possible worlds based on new information. Recent work by van Ditmarsch, French and Pinchinat has presented an axiomatization and complexity results for refinement quantifiers in the general modal logic K. Here we extend these results to apply to the epistemic and doxastic settings for a single agent.