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Intuitionistic logic freed of all metarules

Published online by Cambridge University Press:  12 March 2014

Giovanna Corsi  and
Gabriele Tassi
Giovanna Corsi
Affiliation:
Dipartimento Di Filosofia, Universitá Di Bologna, Via Zamboni, 38, 1-40126 Bologna, Italy. E-mail: [email protected]
Gabriele Tassi
Affiliation:
Dipartimento Di Filosofia, Universitá Di Bologna, Via Zamboni, 38, 1-40126 Bologna, Italy. E-mail: [email protected]
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Abstract

In this paper we present two calculi for intuitionistic logic. The first one. IG, is characterized by the fact that every proof-search terminates and termination is reached without jeopardizing the subformula property. As to the second one, SIC, proof-search terminates, the subformula property is preserved and moreover proof-search is performed without any recourse to metarules, in particular there is no need to back-track. As a consequence, proof-search in the calculus SIC is accomplished by a single tree as in classical logic.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 4 , December 2007 , pp. 1204 - 1218
Copyright
Copyright © Association for Symbolic Logic 2007

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References

REFERENCES

[1]Avron, A., A constructive analysis of RM, this Journal, vol. 52 (1987), pp. 939–951.Google Scholar
[2]Corsi, G., Semantic trees for Dummett's logic LC, Studio Logica, vol. 45 (1986), pp. 199–206.CrossRefGoogle Scholar
[3]Corsi, G., The a fortiori rule: The key to reach termination in intuitionistic logic. Logic and Philosophy in Italy, Some trends and perspectives (Franchella, M. and Bailo, E., editors), Polimetrica, Milano, 2006, pp. 26–47.Google Scholar
[4]Dyckhoff, R., Contraction-free sequent calculi for intuitionistic logic, this Journal, vol. 57 (1992), pp. 795–807.Google Scholar
[5]Heuerding, A., Seyfried, M., and Zimmermann, H., Efficient loop-check for backward proof search in some non-classical prepositional logics. Proceedings of TABLEAUX'96, Lecture Notes on Computer Science, vol. 1071, Springer, 1996.Google Scholar
[6]Pottinger, G., Uniform cut-free formulations of T, S4 and S5, this Journal, vol. 48 (1992), p. 900.Google Scholar
[7]Troelstra, A. and Schwichtenberg, H., Basic Proof Theory, Cambridge University Press, 1996, 2nd edition in 2000.Google Scholar