Abstract
In this paper, we introduce prefixed tableau systems for logics combining Artemov’s logic of proofs, which is introduced in order to explore combinatorial structure of proofs, and the logic of provability (strong provability), which has been studied as a logic of formal provability (provability and truth) in arithmetic for decades. Such joint logics have already been studied, but no cut-free tableau systems for these logics have been available in the literature so far. We show the admissibility of cut for these systems via semantic completeness for cut-free prefixed tableau systems for these logics.
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Kurokawa, H. (2013). Prefixed Tableau Systems for Logic of Proofs and Provability. In: Galmiche, D., Larchey-Wendling, D. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2013. Lecture Notes in Computer Science(), vol 8123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40537-2_18
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DOI: https://doi.org/10.1007/978-3-642-40537-2_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40536-5
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