Why Intuitionistic Relevant Logic Cannot Be a Core Logic

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.