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NORMAL DERIVABILITY IN CLASSICAL NATURAL DEDUCTION

Published online by Cambridge University Press:  05 March 2012

JAN VON PLATO  and
ANNIKA SIDERS
JAN VON PLATO*
Affiliation:
Department of Philosophy, University of Helsinki
ANNIKA SIDERS*
Affiliation:
Department of Philosophy, University of Helsinki
*
*DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF HELSINKI, 00014 UNIVERSITY OF HELSINKI, HELSINKI, FINLAND E-mail: jan.vonplato@helsinki.fi
†DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF HELSINKI, 00014 UNIVERSITY OF HELSINKI, HELSINKI, FINLAND E-mail: annika.siders@helsinki.fi
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Abstract

A normalization procedure is given for classical natural deduction with the standard rule of indirect proof applied to arbitrary formulas. For normal derivability and the subformula property, it is sufficient to permute down instances of indirect proof whenever they have been used for concluding a major premiss of an elimination rule. The result applies even to natural deduction for classical modal logic.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 5 , Issue 2 , June 2012 , pp. 205 - 211
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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