Journal of Symbolic Logic 66 (4):1803-1816 (2001)
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| Abstract |
A sequent calculus is given in which the management of weakening and contraction is organized as in natural deduction. The latter has no explicit weakening or contraction, but vacuous and multiple discharges in rules that discharge assumptions. A comparison to natural deduction is given through translation of derivations between the two systems. It is proved that if a cut formula is never principal in a derivation leading to the right premiss of cut, it is a subformula of the conclusion. Therefore it is sufficient to eliminate those cuts that correspond to detour and permutation conversions in natural deduction.
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| DOI | 10.2307/2694976 |
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References found in this work BETA
Natural Deduction: A Proof-Theoretical Study.Richmond Thomason - 1965 - Journal of Symbolic Logic 32 (2):255-256.
The Collected Papers of Gerhard Gentzen.K. Schütte - 1972 - Journal of Symbolic Logic 37 (4):752-753.
Natural Deduction with General Elimination Rules.Jan von Plato - 2001 - Archive for Mathematical Logic 40 (7):541-567.
A Proof of Gentzen's Hauptsatz Without Multicut.Jan von Plato - 2001 - Archive for Mathematical Logic 40 (1):9-18.
Citations of this work BETA
Harmony in Multiple-Conclusion Natural-Deduction.Nissim Francez - 2014 - Logica Universalis 8 (2):215-259.
Translations Between Gentzen–Prawitz and Jaśkowski–Fitch Natural Deduction Proofs.Shawn Standefer - 2019 - Studia Logica 107 (6):1103-1134.
Natural Deduction Systems for Nelson's Paraconsistent Logic and its Neighbors.Norihiro Kamide - 2005 - Journal of Applied Non-Classical Logics 15 (4):405-435.
Combinatorial Analysis of Proofs in Projective and Affine Geometry.Jan von Plato - 2010 - Annals of Pure and Applied Logic 162 (2):144-161.
View all 9 citations / Add more citations
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