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Logic Journal of IGPL Advance Access published online on October 12, 2007
Logic Journal of IGPL, doi:10.1093/jigpal/jzm048
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© The Author, 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

A Note on Gentzen's LJ and NJ Systems Isomorphism

Wagner De Campos Sanz

Dept. Filosofia, Universidade Federal de Goiás, Campus II Samambaia, Goiânia,GO, C.P. 131, CEP 74001-970, Brazil, E-mail: sanz{at}fchf.ufg.br


  Abstract

In this paper we are going to examine intuitionistic sequent calculus and its negation rules. We state new negation rules defining, in this way, a new sequent system. It will be used to clarify Gentzen's NJ and LJ systems isomorphism. These new negation rules are a direct reading of new natural deduction negation rules obtained by a slight modification of NJ rules. We also show that the new system is equivalent to LJ and that the Hauptsatz holds for it.

Key Words: negation rules • intuitionist sequent calculus • negation • absurd

Received for publication 15 September 2006.
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