Undecidability for arbitrary public announcement logic

Arbitrary public announcement logic (APAL) is an extension of multi-agent epistemic logic that allows agents’ knowledge states to be updated by the public announcement of (possibly arbitrary) epistemic formulae. It has been shown to be more expressive than epistemic logic, and a sound and complete axiomatization has been given. Here we address the question of decidability. We present a proof that the satisfiability problem for arbitrary public announcement logic (APAL) is co-RE complete, via a tiling argument.