Dynamic Deontic Logic for Permitted Announcements

In this paper, we introduce and study a dynamic deontic logic for permitted announcements. In our logic framework, it is permitted to announce something if announcing it would not lead to forbidden knowledge. It is shown that the logic is not compact, and we propose a sound and weakly complete Hilbert-style axiomatisation. We also study the computational complexity of the model checking problem and the decidability of the satisfiability problem. Finally, we introduce a neighbourhood semantics with a strongly complete axiomatisation.