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Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic via Linear Nested Sequents

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Logical Foundations of Computer Science (LFCS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11972))

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Abstract

This paper employs the linear nested sequent framework to design a new cut-free calculus (\(\mathsf {LNIF}\)) for intuitionistic fuzzy logic—the first-order Gödel logic characterized by linear relational frames with constant domains. Linear nested sequents—which are nested sequents restricted to linear structures—prove to be a well-suited proof-theoretic formalism for intuitionistic fuzzy logic. We show that the calculus \(\mathsf {LNIF}\) possesses highly desirable proof-theoretic properties such as invertibility of all rules, admissibility of structural rules, and syntactic cut-elimination.

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Notes

  1. 1.

    We refer to [28] for a detailed discussion of fundamental proof-theoretic properties.

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Acknowledgments

The author would like to thank his supervisor A. Ciabattoni for her continued support, B. Lellmann for his thought-provoking discussions on linear nested sequents, and K. van Berkel for his helpful comments. Work funded by FWF projects I2982, Y544-N2, and W1255-N23.

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Authors and Affiliations

  1. Institut für Logic and Computation, Technische Universität Wien, 1040, Vienna, Austria

    Tim Lyon

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  1. Tim Lyon
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Correspondence to Tim Lyon .

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Editors and Affiliations

  1. The Graduate Center, CUNY, New York, NY, USA

    Sergei Artemov

  2. Cornell University, Ithaca, NY, USA

    Anil Nerode

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Lyon, T. (2020). Syntactic Cut-Elimination for Intuitionistic Fuzzy Logic via Linear Nested Sequents. In: Artemov, S., Nerode, A. (eds) Logical Foundations of Computer Science. LFCS 2020. Lecture Notes in Computer Science(), vol 11972. Springer, Cham. https://doi.org/10.1007/978-3-030-36755-8_11

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