Abstract
The paper introduces Hilbert– and Gentzen-style calculi which correspond to systems \({\mathsf{C}_{n}}\) from Gupta and Belnap [3]. Systems \({\mathsf{C}_{n}}\) were shown to be sound and complete with respect to the semantics of finite revision. Here, it is shown that Gentzen-style systems \({\mathsf{GC}_{n}}\) admit a syntactic proof of cut elimination. As a consequence, it follows that they are consistent.
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References
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Bruni, R. Analytic Calculi for Circular Concepts by Finite Revision. Stud Logica 101, 915–932 (2013). https://doi.org/10.1007/s11225-012-9402-2
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DOI: https://doi.org/10.1007/s11225-012-9402-2