Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-20T14:29:25.391Z Has data issue: false hasContentIssue false
  • English
  • Français

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: corsi@philo.unibo.it
Gabriele Tassi
Affiliation:
Dipartimento Di Filosofia, Universitá Di Bologna, Via Zamboni, 38, 1-40126 Bologna, Italy. E-mail: gabriele.tassi@studio.unibo.it
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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