Strong Cut-Elimination Systems for Hudelmaier’s Depth-Bounded Sequent Calculus for Implicational Logic

  • Roy Dyckhoff
  • Delia Kesner
  • Stéphane Lengrand
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4130)


Inspired by the Curry-Howard correspondence, we study normalisation procedures in the depth-bounded intuitionistic sequent calculus of Hudelmaier (1988) for the implicational case, thus strengthening existing approaches to Cut-admissibility. We decorate proofs with terms and introduce various term-reduction systems representing proof transformations. In contrast to previous papers which gave different arguments for Cut-admissibility suggesting weakly normalising procedures for Cut-elimination, our main reduction system and all its variations are strongly normalising, with the variations corresponding to different optimisations, some of them with good properties such as confluence.


Intuitionistic Logic Reduction System Reduction Rule Sequent Calculus Denotational Semantic 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Roy Dyckhoff
    • 1
  • Delia Kesner
    • 2
  • Stéphane Lengrand
    • 1
    • 2
  1. 1.School of Computer ScienceUniversity of St AndrewsScotland
  2. 2.PPS, CNRS and Université Paris 7France

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