A General Framework for Modal Correspondence in Dynamic Epistemic Logic.

We introduce a unified framework for dynamic epistemic logics, which in particular encompasses Public Announcement Logic (PAL), Epistemic Action (EA) and Preference Upgrade (PU). Our framework consists of a generic language, in which some of the known reduction axioms are expressible, together with relational and algebraic semantics. We then establish correspondences between generic reduction axioms and semantic properties, in both relational and algebraic settings. This leads to alternative proofs of the completeness of PAL, EA, PU with respect to their relational semantics and algebraic semantics (for the former two).