On the Complexity of Dynamic Epistemic Logic

Although Dynamic Epistemic Logic (DEL) is an influential logical framework for representing and reasoning about information change, little is known about the computational complexity of its associated decision problems. In fact, we only know that for public announcement logic, a fragment of DEL, the satisfiability problem and the model-checking problem are respectively PSPACE-complete and in P. We contribute to fill this gap by proving that for the DEL language with event models, the model-checking problem is, surprisingly, PSPACE-complete. Also, we prove that the satisfiability problem is NEXPTIME-complete. In doing so, we provide a sound and complete tableau method deciding the satisfiability problem.