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