Dynamic Probability Logic and its Innitary Extension

In this paper, we introduce the nitary dynamic probability logic (DPL), as well as its innitary extension DPL_w1 . Both these logics extend the (modal) probability logic (PL) by adding a temporal-like operator [ which describes the dynamic part of the system. We subsequently provide Hilbert-style axiomatizations for both DPL and DPL 1 . Weshow that while the proposed axiomatization for DPL is strongly complete, the axiomatization for the innitary counterpart supplies strong completeness for each countable fragment A of DPL 1 . Moreover, we show that some dynamic properties such as measure-preserving, ergodicity and mixing are de nable within DPL and DPL 1