A simple proof that super-consistency implies cut elimination

Authors:
Gilles Dowek;Olivier Hermant
Affiliations:
École Polytechnique and INRIA, LIX, École Polytechnique, Palaiseau Cedex, France;PPS, Université Denis Diderot, Paris Cedex 05, France
Venue:
RTA'07 Proceedings of the 18th international conference on Term rewriting and applications
Year:
2007

Citing 7
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Abstract

We give a simple and direct proof that super-consistency implies cut elimination in deduction modulo. This proof can be seen as a simplification of the proof that super-consistency implies proof normalization. It also takes ideas from the semantic proofs of cut elimination that proceed by proving the completeness of the cut free calculus. In particular, it gives a generalization, to all super-consistent theories, of the notion of V-complex, introduced in the semantic cut elimination proofs for simple type theory.