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Proofs of strong normalisation for second order classical natural deduction

Published online by Cambridge University Press:  12 March 2014

Michel Parigot
Michel Parigot*
Affiliation:
Equipe de Logique—CNRS UA 753, 45-55 5Ème Étage, Université Paris7, 2 Place Jussieu, 75251 Paris Cedex 05, France E-mail: parigot@logique.jussieu.fr
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Abstract

We give two proofs of strong normalisation for second order classical natural deduction. The first one is an adaptation of the method of reducibility candidates introduced in [9] for second order intuitionistic natural deduction; the extension to the classical case requires in particular a simplification of the notion of reducibility candidate. The second one is a reduction to the intuitionistic case, using a Kolmogorov translation.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 4 , December 1997 , pp. 1461 - 1479
Copyright
Copyright © Association for Symbolic Logic 1997

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