The Set of Probabilistic Algorithmic Formulas Valid in a Finite Structure Is Decidable with Respect to Its Diagram

Abstract

In the paper it is considered a probabilistic logic of programs PrAL, similar to the Feldman-Harel logic, constructed for expressing properties of iterative programs with operations $\mathit{x}:=?$ , either … or … interpreted in a probabilistic way. A language of PrAL contains a sort of variables interpreted as real numbers, used to describe probabilities of behaviours of programs. The main result states that the set of formulas of PrAL valid in a finite structure is decidable with respect to the diagram of the structure.