The content discusses cut elimination for cyclic proofs in the context of modal logic extended with the 'eventually' temporal operator. The key points are:
The authors consider modal logic MLe, which extends basic modal logic with the 'eventually' (F) operator. They provide a complete cyclic sequent calculus GKe for this logic.
The main challenge in cut elimination for cyclic proofs is that cuts can interfere with the global validity condition that ensures soundness of cyclic reasoning. The authors distinguish between "unimportant" cuts, which can be eliminated by standard techniques, and "important" cuts, which require a more involved treatment.
For important cuts, the authors develop a reductive cut-elimination procedure that works directly on cyclic proofs. This involves transforming the proof into a "traversed proof" representation, where cuts are isolated and can be eliminated recursively.
The authors show that their cut-elimination procedure preserves the cyclic structure of the proof, directly producing a cut-free cyclic proof without the need for intermediate steps to regularize the proof.
The work is presented as a case study, with the authors noting that the techniques developed here could potentially be applied to cut elimination for cyclic proofs in other modal fixpoint logics.
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Önemli Bilgiler Şuradan Elde Edildi
by Bahareh Afsh... : arxiv.org 05-06-2024
https://arxiv.org/pdf/2405.01935.pdfDaha Derin Sorular