Optimal Regression for Reasoning about Knowledge and Actions (long version)

We show how in the propositional case both Reiter’s and Scherl & Levesque’s solutions to the frame problem can be modelled in dynamic epistemic logic (DEL), and provide an optimal regression algorithm for the latter. Our method is as follows: we extend Reiter’s framework by integrating observation actions and modal operators of knowledge, and encode the resulting formalism in DEL with announcement and assignment operators. By extending Lutz’ recent satisfiability-preserving reduction to our logic, we establish optimal decision procedures for both Reiter’s and Scherl & Levesque’s approaches: satisfiability is NP-complete for one agent, PSPACE-complete for multiple agents and EXPTIME-complete when common knowledge is involved.