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Translations from natural deduction to sequent calculus

✍ Scribed by Jan von Plato

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 96 KB
Volume: 49
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200310047

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✦ Synopsis

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.

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