Abstract

In the paper the joint Logic of Proofs and Provability is presented that incorporates both the modality □ for provability 287–304) and the proof operator tF representing the proof predicate “t is a proof of F” . The obtained system naturally includes both the modal logic of provability GL and Artemov's Logic of Proofs . The presence of the modality □ requires two new operations on proofs that together with operations of allow to realize all the invariant operations on proofs admitting description in the modal propositional language. Logic is proved to be decidable and complete with the intended provability semantics