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References (10)
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M. Borisavljevic (1999)
A Cut-Elimination Proof in Intuitionistic Predicate LogicAnn. Pure Appl. Log., 99
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G. Gentzen (1935)
Untersuchungen über das logische Schließen. IMathematische Zeitschrift, 39
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Garrel Pottinger (1977)
Normalization as a homomorphic image of cut-eliminationAnnals of Mathematical Logic, 12
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G. Pottinger (1977)
Normalization as a homomorrhic image of cut eliminationAnnals of Pure and Applied Logic, 12
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D. Prawitz (1971)
Ideas and Results in Proof TheoryStudies in logic and the foundations of mathematics, 63
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J. Zucker (1974)
The correspondence between cut-elimination and normalization IIAnnals of Mathematical Logic, 7
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J. Plato (2001)
A proof of Gentzen's Hauptsatz without multicutArch. Math. Log., 40
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G. Gentzen, M. Szabo (1969)
The collected papers of Gerhard Gentzen -
M. Borisavljevic (2003)
Two measures for proving Gentzen's Hauptsatz without mixArchive for Mathematical Logic, 42
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M. Borisavljevic, K. Dosen, Z. Petric (1999)
On permuting cut with contractionMathematical Structures in Computer Science, 10
- Publisher
- Springer Journals
- Copyright
- Copyright © 2005 by Springer-Verlag Berlin Heidelberg
- Subject
- Mathematics; Mathematics, general; Algebra; Mathematical Logic and Foundations
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-005-0295-x
- Publisher site
- See Article on Publisher Site
Abstract
A new set of conversions for derivations in the system of sequents for intuitionistic predicate logic will be defined. These conversions will be some modifications of Zucker's conversions from the system of sequents [InlineMediaObject not available: see fulltext.] from [11], which will have the following characteristics: (1) these conversions will be sufficient for transforming a derivation into a cut-free one, and (2) in the natural deduction the image of each of these conversions will be either in the set of conversions for normalization procedure, or an identity of derivations. This will be used to give a new proof of the normalization theorem for natural deduction, as a consequence of the cut-elimination theorem for the system of sequents.
Journal
Archive for Mathematical Logic – Springer Journals
Published: Sep 27, 2005