An algorithm for detection of ultra-weak completeness of the systems of formulas in a provability logic of propositions

Abstract

We consider the problem of completeness relative to ultra-weak expressibility of the systems of formulas in the simplest non-trivial extension of the propositional provability logic. We propose an algorithm to address this problem. It is a first step toward investigation of this problem in propositional provability logic. A similar problem was considered by prof. Mefodie Rat¸˘a in the case of the intuitionistic logic.