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Proof normalization modulo
Journal of Symbolic Logic 68 (4):1289-1316 (2003)
Abstract
We define a generic notion of cut that applies to many first-order theories. We prove a generic cut elimination theorem showing that the cut elimination property holds for all theories having a so-called pre-model. As a corollary, we retrieve cut elimination for several axiomatic theories, including Church's simple type theory.Other Versions
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Citations of this work
Are Uniqueness and Deducibility of Identicals the Same?Alberto Naibo & Mattia Petrolo - 2014 - Theoria 81 (2):143-181.
Some general results about proof normalization.Marc Aiguier & Delphine Longuet - 2010 - Logica Universalis 4 (1):1-29.
A Simple Proof that Super-Consistency Implies Cut Elimination.Gilles Dowek & Olivier Hermant - 2012 - Notre Dame Journal of Formal Logic 53 (4):439-456.
On the convergence of reduction-based and model-based methods in proof theory.Gilles Dowek - 2009 - Logic Journal of the IGPL 17 (5):489-497.
References found in this work
A Mathematical Introduction to Logic.Herbert Enderton - 2001 - Bulletin of Symbolic Logic 9 (3):406-407.
A Computational Logic.Robert S. Boyer & J. Strother Moore - 1990 - Journal of Symbolic Logic 55 (3):1302-1304.
Typed Lambda calculi. S. Abramsky et AL.H. P. Barendregt - 1992 - In S. Abramsky, D. Gabbay & T. Maibaurn, Handbook of Logic in Computer Science. Oxford University Press. pp. 117--309.
Per Martin-Löf. Intuitionistic type theory. Studies in proof theory. Bibliopolis, Naples1984, ix + 91 pp. [REVIEW]W. A. Howard - 1986 - Journal of Symbolic Logic 51 (4):1075-1076.
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