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On the non-confluence of cut-elimination

Published online by Cambridge University Press:  12 March 2014

Matthias Baaz  and
Stefan Hetzl
Matthias Baaz
Affiliation:
Institute of Discrete Mathematics and Geometry (E104), Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040 Vienna, Austria, E-mail: baaz@logic.at
Stefan Hetzl
Affiliation:
Laboratoire Preuves, Programmes et Systèmes (PPS), Université Paris Diderot– Paris 7, 175 Rue du Chevaleret, 75013 Paris, France, E-mail: stefan.hetzl@pps.jussieu.fr
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Abstract

We study cut-elimination in first-order classical logic. We construct a sequence of polynomial-length proofs having a non-elementary number of different cut-free normal forms. These normal forms are different in a strong sense: they not only represent different Herbrand-disjunctions but also differ in their prepositional structure.

This result illustrates that the constructive content of a proof in classical logic is not uniquely determined but rather depends on the chosen method for extracting it.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 1 , March 2011 , pp. 313 - 340
Copyright
Copyright © Association for Symbolic Logic 2011

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