Confluence as a Cut Elimination Property

  • Gilles Dowek
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2706)


The goal of this note is to compare two notions, one coming from the theory of rewrite systems and the other from proof theory: confluence and cut elimination. We show that to each rewrite system on terms, we can associate a logical system: asymmetric deduction modulo this rewrite system and that the confluence property of the rewrite system is equivalent to the cut elimination property of the associated logical system. This equivalence, however, does not extend to rewrite systems directly rewriting atomic propositions.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Gilles Dowek
    • 1
  1. 1.École polytechnique and INRIALIX, École polytechniquePalaiseau CedexFrance

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