Notre Dame Journal of Formal Logic

Why Intuitionistic Relevant Logic Cannot Be a Core Logic

Joseph Vidal-Rosset

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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}

intuitionistic logic relevant logic minimal logic


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.

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