Dynamic Probability Logic: Decidability & Computability

In this article, the decidability and computability issues of dynamic probability logic (DPL) are addressed. Firstly, a proof system ${\mathcal{H}}_{DPL}$ is introduced for DPL and shown that it is weakly complete. Furthermore, this logic has the finite model property and so is decidable. Secondly, a strongly complete proof system HDPL is presented for DPL and proved that its canonical model is a computable structure.