Reducing dynamic epistemic logic to PDL by program transformation

We present a direct reduction of dynamic epistemic logic in the spirit of Baltag, Moss and Solecki to propositional dynamic logic (PDL) by program transformation. The program transformation approach associates with every update action a transformation on PDL programs. These transformations are then employed in reduction axioms for the update actions. It follows that the logic of public announcement, the logic of group announcements, the logic of secret message passing, and so on, can all be viewed as subsystems of PDL. Moreover, the program transformation approach can be used to generate the appropriate reduction axioms for these logics. Our direct reduction of dynamic epistemic logic to PDL was inspired by the reduction of dynamic epistemic logic to automata PDL of Van Benthem and Kooi Our approach shows how the detour through automata can be avoided