Normal derivations and sequent derivations

Journal of Philosophical Logic 37 (6):521 - 548 (2008)

The well-known picture that sequent derivations without cuts and normal derivations “are the same” will be changed. Sequent derivations without maximum cuts (i.e. special cuts which correspond to maximum segments from natural deduction) will be considered. It will be shown that the natural deduction image of a sequent derivation without maximum cuts is a normal derivation, and the sequent image of a normal derivation is a derivation without maximum cuts. The main consequence of that property will be that sequent derivations without maximum cuts and normal derivations “are the same”.
Keywords cut elimination  normalization
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DOI 10.1007/s10992-008-9084-4
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Basic Proof Theory.A. S. Troelstra - 2000 - Cambridge University Press.
A Proof of Gentzen's Hauptsatz Without Multicut.Jan von Plato - 2001 - Archive for Mathematical Logic 40 (1):9-18.
Cut-Elimination and Normalization.J. Zucker - 1974 - Annals of Pure and Applied Logic 7 (1):1.
Normalization as a Homomorphic Image of Cut-Elimination.Garrel Pottinger - 1977 - Annals of Pure and Applied Logic 12 (3):323.

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