Notre Dame Journal of Formal Logic

Why Intuitionistic Relevant Logic Cannot Be a Core Logic

Joseph Vidal-Rosset

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Abstract

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

Article information

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

Dates
Received: 26 January 2014
Accepted: 30 July 2014
First available in Project Euclid: 4 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1486177446

Digital Object Identifier
doi:10.1215/00294527-3839326

Mathematical Reviews number (MathSciNet)
MR3634979

Zentralblatt MATH identifier
06751301

Subjects
Primary: 03B20: Subsystems of classical logic (including intuitionistic logic) 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) {For proof-theoretic aspects see 03F52}

Keywords
intuitionistic logic relevant logic minimal logic

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


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References

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