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Proofs of strong normalisation for second order classical natural deduction
Journal of Symbolic Logic 62 (4):1461-1479 (1997)
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 translationLinks
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Citations of this work
Structural Rules in Natural Deduction with Alternatives.Greg Restall - 2023 - Bulletin of the Section of Logic 52 (2):109-143.
Non-strictly positive fixed points for classical natural deduction.Ralph Matthes - 2005 - Annals of Pure and Applied Logic 133 (1):205-230.
Church–Rosser property of a simple reduction for full first-order classical natural deduction.Y. Andou - 2003 - Annals of Pure and Applied Logic 119 (1-3):225-237.
Strong normalization of classical natural deduction with disjunctions.Koji Nakazawa & Makoto Tatsuta - 2008 - Annals of Pure and Applied Logic 153 (1-3):21-37.
Call-by-name reduction and cut-elimination in classical logic.Kentaro Kikuchi - 2008 - Annals of Pure and Applied Logic 153 (1-3):38-65.
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