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A SEQUENT CALCULUS ISOMORPHIC TO GENTZEN’S NATURAL DEDUCTION

Published online by Cambridge University Press:  13 September 2010

JAN VON PLATO
JAN VON PLATO*
Affiliation:
Department of Philosophy, University of the Helsinki
*
*DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF HELSINKI, 00014 U. OF HELSINKI, FINLAND. E-mail:jan.vonplato@helsinki.fi
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Abstract

Gentzen’s thesis proved the equivalence of natural deduction, sequent calculus, and axiomatic logic through a cycle of translations. Mysteriously, even normal derivations in natural deduction got translated into sequent derivations with cuts. It is shown that the insertion of special cuts, whenever left conjunction, left implication, or left universal quantification in sequent calculus is used, results in sequent calculus derivations isomorphic to those in Gentzen’s natural deduction. Thereby the appearance of the cuts in translation is explained.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 4 , Issue 1 , March 2011 , pp. 43 - 53
Copyright
Copyright © Association for Symbolic Logic 2010

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References

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