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A realization theorem for the modal logic of transitive closure K+
Izvestiya. Mathematics. 2025. Vol. 89. No. 2. P. 399–421.
We present a justification logic corresponding to the modal logic of transitive closure K+ and establish a normal realization theorem relating these two systems. The result is obtained by means of a sequent calculus allowing non-well-founded proofs.
Language:
English
Publication based on the results of:
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We consider an extension of the modal logic of transitive closure K+ with certain infinitary derivations and present a sequent calculus for this extension, which allows non-well-founded proofs. We establish continuous cut-elimination for the given calculus using fixed-point theorems for contractive mappings. The infinitary derivations mentioned above are well founded and countably branching, while the non-well-founded proofs ...
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We consider an extension of the modal logic of transitive closure K+ with some inifinitary derivations and present a sequent calculus for this extension, which allows non-well-founded proofs. For the given calculus, we obtain the cut-elimination theorem following the lines of so called continuous cut elimination. Our consideration also covers ordinary proofs of K+ since ...
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