Arbitrary Public Announcement Logic with Mental Programs

We propose a variant of arbitrary public announcement logic which is decidable. In this variant, knowledge accessibility relations are defined by programs. Technically, programs are written in dynamic logic with propositional assignments. We prove that both the model checking problem and the satisfiability problem are decidable and AEXP pol-complete where AEXP pol is the class of decision problems decided by alternating Turing machines running in exponential time where the number of alternations is polynomial. Whereas arbitrary public announcement logic is undecidable, our framework is decidable and we provide a proof-of-concept to show its expressiveness: we use our framework to reason about epistemic properties and arbitrary announcements when agents are cameras located in the plane.