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Original Paper
Translations from natural deduction to sequent calculus
Article first published online: 3 JUL 2003
DOI: 10.1002/malq.200310047
Copyright © 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
1521-3870/asset/cover.gif?v=1&s=3df32dbed8d9153ac6eafe1eaa786854b9b48345 "Mathematical Logic Quarterly")
Additional Information
How to Cite
von Plato, J. (2003), Translations from natural deduction to sequent calculus. Mathematical Logic Quarterly, 49: 435–443. doi: 10.1002/malq.200310047
Publication History
- Issue published online: 3 JUL 2003
- Article first published online: 3 JUL 2003
- Manuscript Accepted: 3 FEB 2003
- Manuscript Received: 12 JUN 2002
- Abstract
- References
- Cited By
Keywords:
- Natural deduction;
- sequent calculus;
- cut rule
Abstract
Gentzen's “Untersuchungen” [1] gave a translation from natural deduction to sequent calculus with the property that normal derivations may translate into derivations with cuts. Prawitz in [8] gave a translation that instead produced cut-free derivations. It is shown that by writing all elimination rules in the manner of disjunction elimination, with an arbitrary consequence, an isomorphic translation between normal derivations and cut-free derivations is achieved. The standard elimination rules do not permit a full normal form, which explains the cuts in Gentzen's translation. Likewise, it is shown that Prawitz' translation contains an implicit process of cut elimination.