How to combine stochastic programming and mathematical theory of programming

In the contribution presented we deal with one method of stochastic programming - probabilistic programming. Probabilistic programming is a method of stochastic programming in which the probabilities of the values of the variables are of interest. Our approach is that scientific problem solving we can construct in logical reasoning over some mathematical theories. In this approach we deal with category theory for construction of type theory and of the logical system. Then we formulate the logical theory to enclose the solution of the problem. These steps we show at well-known examples: the random number generator, the Blackjack game and the Monty Hall problem.