Journal of Symbolic Logic 66 (4):1803-1816 (2001)

Authors
Jan Von Plato
University of Helsinki
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.

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Citations of this work BETA

Harmony in Multiple-Conclusion Natural-Deduction.Nissim Francez - 2014 - Logica Universalis 8 (2):215-259.
Varieties of Linear Calculi.Sara Negri - 2002 - Journal of Philosophical Logic 31 (6):569-590.
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.

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