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A Multiple-Conclusion Calculus for First-Order Gödel Logic

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Computer Science – Theory and Applications (CSR 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6651))

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Abstract

We present a multiple-conclusion hypersequent system for the standard first-order Gödel logic. We provide a constructive, direct, and simple proof of the completeness of the cut-free part of this system, thereby proving both completeness for its standard semantics, and the admissibility of the cut rule in the full system. The results also apply to derivations from assumptions (or “non-logical axioms”), showing that such derivations can be confined to those in which cuts are made only on formulas which occur in the assumptions. Finally, the results about the multiple-conclusion system are used to show that the usual single-conclusion system for the standard first-order Gödel logic also admits (strong) cut-admissibility.

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Author information

Authors and Affiliations

  1. School of Computer Science, Tel-Aviv University, Israel

    Arnon Avron & Ori Lahav

Authors
  1. Arnon Avron
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  2. Ori Lahav
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Editor information

Editors and Affiliations

  1. Steklov Institute of Mathematics at St. Petersburg, 27 Fontanka, 191023, St.Petersburg, Russia

    Alexander Kulikov

  2. Department of Mathematical Logic and Theory of Algorithms, Moscow State University, Leninskie gory, 119991, Moscow, Russia

    Nikolay Vereshchagin

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Avron, A., Lahav, O. (2011). A Multiple-Conclusion Calculus for First-Order Gödel Logic. In: Kulikov, A., Vereshchagin, N. (eds) Computer Science – Theory and Applications. CSR 2011. Lecture Notes in Computer Science, vol 6651. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20712-9_36

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  • DOI: https://doi.org/10.1007/978-3-642-20712-9_36

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20711-2

  • Online ISBN: 978-3-642-20712-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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