We start from Reiter's solution to the frame problem in terms of successor state axioms and Scherl& Levesque's extension to knowledge, as formulated by Lakemeyer&Levesque in their logic ES. While it was believed up to now that quantification over actions is a characteristic feature of Reiter's solution, we here show that for a reasonably large subset of Reiter?s basic action theories one can do without. We do so by recasting restricted basic action theories in a propositional modal logic, viz. dynamic epistemic logic with public announcements and public assignments.