The probability theory is a well-studied branch of mathematics, in order to
carry out formal reasoning about probability. Thus, it is important to have a
logic, both for computation of probabilities and for reasoning about
probabilities, with a well-defined syntax and semantics. Both current
approaches, based on Nilsson's probability structures/logics, and on linear
inequalities in order to reason about probabilities, have some weak points. In
this paper we have presented the complete revision of both approaches.