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A Connection Between Cut Elimination and Normalization

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Abstract

A new set of conversions for derivations in the system of sequents for intuitionistic predicate logic will be defined. These conversions will be some modifications of Zucker's conversions from the system of sequents from [11], which will have the following characteristics: (1) these conversions will be sufficient for transforming a derivation into a cut-free one, and (2) in the natural deduction the image of each of these conversions will be either in the set of conversions for normalization procedure, or an identity of derivations. This will be used to give a new proof of the normalization theorem for natural deduction, as a consequence of the cut-elimination theorem for the system of sequents.

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Authors and Affiliations

  1. Faculty of Transport and Traffic Engineering, University of Belgrade, Vojvode Stepe 305, 11000, Belgrade, Serbia and Montenegro

    Mirjana Borisavljević

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  1. Mirjana Borisavljević
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Correspondence to Mirjana Borisavljević.

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Received: January 2003

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Borisavljević, M. A Connection Between Cut Elimination and Normalization. Arch. Math. Logic 45, 113–148 (2006). https://doi.org/10.1007/s00153-005-0295-x

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  • DOI: https://doi.org/10.1007/s00153-005-0295-x

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