Abstract
In the paper the joint Logic of Proofs and Provability LPP is presented that incorporates both the modality □ for provability (Israel J. Math. 25 (1976) 287–304) and the proof operator 〚t〛F representing the proof predicate “ t is a proof of F” (Technical Report No. CFIS 95-29, Cornell University, 1995). The obtained system LPP naturally includes both the modal logic of provability GL and Artemov's Logic of Proofs LP . The presence of the modality □ requires two new operations on proofs that together with operations of LP allow to realize all the invariant operations on proofs admitting description in the modal propositional language. Logic LPP is proved to be decidable and complete with the intended provability semantics.
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