## Notre Dame Journal of Formal Logic

### Why Intuitionistic Relevant Logic Cannot Be a Core Logic

Joseph Vidal-Rosset

#### Abstract

At the end of the 1980s, Tennant invented a logical system that he called “intuitionistic relevant logic” ($\mathbf{IR}$, for short). Now he calls this same system “Core logic.” In Section 1, by reference to the rules of natural deduction for $\mathbf{IR}$, I explain why $\mathbf{IR}$ is a relevant logic in a subtle way. Sections 2, 3, and 4 give three reasons to assert that $\mathbf{IR}$ cannot be a core logic.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 58, Number 2 (2017), 241-248.

Dates
Accepted: 30 July 2014
First available in Project Euclid: 4 February 2017

https://projecteuclid.org/euclid.ndjfl/1486177446

Digital Object Identifier
doi:10.1215/00294527-3839326

Mathematical Reviews number (MathSciNet)
MR3634979

Zentralblatt MATH identifier
06751301

#### Citation

Vidal-Rosset, Joseph. Why Intuitionistic Relevant Logic Cannot Be a Core Logic. Notre Dame J. Formal Logic 58 (2017), no. 2, 241--248. doi:10.1215/00294527-3839326. https://projecteuclid.org/euclid.ndjfl/1486177446

#### References

• [1] David, R., K. Nour, and C. Raffalli, Introduction à la logique (Théorie de la démonstration, cours et exercices corrigés), Dunod, Paris, 2003.
• [2] Leibniz, G. W., Recherches générales sur l’analyse des notions et des vérités: 24 thèses métaphysiques et autres textes logiques et métaphysiques, edited by J.-B. Rauzy, Presses universitaires de France, Paris, France, 1998.
• [3] Prawitz, D., Natural Deduction—A Proof Theoretical Study, 2nd ed., Dover, Mineola, N.Y., 2006.
• [4] Tennant, N., Autologic, Edinburgh University Press, Edinburgh, 1992.
• [5] Tennant, N., The Taming of the True, Oxford University Press, New York, 1997.
• [6] Tennant, N., “Ultimate Normal Forms for Parallelized Natural Deductions,” Logic Journal of the IGPL, vol. 10 (2002), pp. 299–337.
• [7] Tennant, N., “Relevance in Reasoning,” pp. 696–726 in The Oxford Handbook of Philosophy of Mathematics and Logic, edited by S. Shapiro, Oxford University Press, Oxford, 2005.