On Herbrand’s Theorem for Intuitionistic Logic

  • Alexander Lyaletski
  • Boris Konev
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4160)


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.


Inference Tree Intuitionistic Logic Sequent Calculus Rule Application Proof Tree 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Alexander Lyaletski
    • 1
  • Boris Konev
    • 2
  1. 1.Faculty of CyberneticsKiev National Taras Shevchenko UniversityUkraine
  2. 2.Department of Computer ScienceUniversity of LiverpoolUnited Kingdom

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