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THE SUBFORMULA PROPERTY IN CLASSICAL NATURAL DEDUCTION ESTABLISHED CONSTRUCTIVELY

Published online by Cambridge University Press:  12 October 2012

TOR SANDQVIST
TOR SANDQVIST*
Affiliation:
Division of Philosophy, Royal Institute of Technology
*
*DIVISION OF PHILOSOPHY, ROYAL INSTITUTE OF TECHNOLOGY, TEKNIKRINGEN 78B, 10044 STOCKHOLM, SWEDEN. E-mail: tor.sandqvist@abe.kth.se
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Abstract

A constructive proof is provided for the claim that classical first-order logic admits of a natural deduction formulation featuring the subformula property.

Type
Research Articles
Information
The Review of Symbolic Logic , Volume 5 , Issue 4 , December 2012 , pp. 710 - 719
Copyright
Copyright © Association for Symbolic Logic 2012

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References

BIBLIOGRAPHY

Gentzen, G. (1969). Investigations into logical deduction. In Szabo, M. E., editor. The Collected Papers of Gerhard Gentzen. Amsterdam: North-Holland Publishing Company, pp. 68–131.Google Scholar
Milne, P. (2008). A formulation of first-order classical logic in natural deduction with the subformula property. In Peliš, M., editor. Logica Yearbook 2007. Prague, Czech Republic: FILOSOFIA–ΦIΛOΣOΦIA, pp. 97–110.Google Scholar
Milne, P. (2010). Subformula and separation properties in natural deduction via small Kripke models. Review of Symbolic Logic, 3, 175–227.Google Scholar
Prawitz, D. (1965). Natural Deduction: A Proof-Theoretical Study. Uppsala, Sweden: Almqvist & Wiksell. Republished in 2006 by Dover Publications.Google Scholar
Segerberg, K. (1983). Arbitrary truth-value functions and natural deduction. Zeitscrift für Logik und Grundlagen der Mathematik, 29, 557–564.Google Scholar