From Gentzen to Jaskowski and Back: Algorithmic Translation of Derivations Between the Two Main Systems of Natural Deduction

Bulletin of the Section of Logic 46 (1/2) (2017)
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Abstract

The way from linearly written derivations in natural deduction, introduced by Jaskowski and often used in textbooks, is a straightforward root-first translation. The other direction, instead, is tricky, because of the partially ordered assumption formulas in a tree that can get closed by the end of a derivation. An algorithm is defined that operates alternatively from the leaves and root of a derivation and solves the problem.

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Jan Von Plato
University of Helsinki

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Natural deduction with general elimination rules.Jan von Plato - 2001 - Archive for Mathematical Logic 40 (7):541-567.

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