A logic for the description of non-deterministic programs and their properties

We present a logic, called Synchronization Tree Logic (STL), for the specification and proof of programs described in a simple term language obtained from a constant Nil by using a set A of unary operators, a binary operator + and recursion. The elements of A represent names of actions, + represents non-deterministic choice, and Nil is the program preforming no action. The language of formulas of the logic proposed, contains the term language used for the description of programs, i.e., programs are formulas of the logic. This provides a uniform frame to deal with programs and their properties as the verification of anassertion t ⊨ f (t is a program, f is a formula) is reduced to the proof of the validity of the formula t ⊃ f. We propose a sound and under some conditions complete deductive system for synchronization tree logics and discuss their relation with modal logics used for the specification of programs