On a Local-Step Cut-Elimination Procedure for the Intuitionistic Sequent Calculus

  • Kentaro Kikuchi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4246)


In this paper we investigate, for intuitionistic implicational logic, the relationship between normalization in natural deduction and cut-elimination in a standard sequent calculus. First we identify a subset of proofs in the sequent calculus that correspond to proofs in natural deduction. Then we define a reduction relation on those proofs that exactly corresponds to normalization in natural deduction. The reduction relation is simulated soundly and completely by a cut-elimination procedure which consists of local proof transformations. It follows that the sequent calculus with our cut-elimination procedure is a proper extension that is conservative over natural deduction with normalization.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Kentaro Kikuchi
    • 1
  1. 1.RIECTohoku UniversitySendaiJapan

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