Confluence as a cut elimination property

Authors:
Gilles Dowek
Affiliations:
École polytechnique and INRIA and LIX, École polytechnique, Palaiseau Cedex, France
Venue:
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Year:
2003

Citing 4
Cited 3

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Abstract

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.