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On Herbrand’s Theorem for Intuitionistic Logic

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Logics in Artificial Intelligence (JELIA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4160))

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Abstract

In this paper we reduce the question of validity of a first-order intuitionistic formula without equality to generating ground instances of this formula and then checking whether the instances are deducible in a propositional intuitionistic tableaux calculus, provided that the propositional proof is compatible with the way how the instances were generated. This result can be seen as a form of the Herbrand theorem, and so it provides grounds for further theoretical investigation of computer-oriented intuitionistic calculi.

Supported by the Nuffield foundation grant NAL/00841/G.

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Author information

Authors and Affiliations

  1. Faculty of Cybernetics, Kiev National Taras Shevchenko University, Ukraine

    Alexander Lyaletski

  2. Department of Computer Science, University of Liverpool, United Kingdom

    Boris Konev

Authors
  1. Alexander Lyaletski
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  2. Boris Konev
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Liverpool, Liverpool, U.K.

    Michael Fisher

  2. University of Liverpool, United Kingdom

    Wiebe van der Hoek

  3. University of Liverpool, Liverpool, UK

    Boris Konev

  4. Department of Computer Science, The University of Liverpool,  

    Alexei Lisitsa

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Lyaletski, A., Konev, B. (2006). On Herbrand’s Theorem for Intuitionistic Logic. In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds) Logics in Artificial Intelligence. JELIA 2006. Lecture Notes in Computer Science(), vol 4160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11853886_25

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  • DOI: https://doi.org/10.1007/11853886_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-39625-3

  • Online ISBN: 978-3-540-39627-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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