Abstract

Dunn–McCall logic $$\mathbf {RM}$$ RM is by far the best understood and the most well-behaved logic in the family of logics developed by the school of Anderson and Belnap. However, it is not considered to be a relevant logic by the relevant logicians, since it fails to have the variable-sharing property. Instead, $$\mathbf {RM}$$ RM is usually characterized as being “semi-relevant,” without explaining what this notion means. In this paper we suggest a plausible definition of semi-relevance, and show that according to it, $$\mathbf {RM}$$ RM is a strongly maximal semi-relevant logic having a conjunction, a disjunction, and an implication. We also review and prove the most important nice properties of $$\mathbf {RM}$$ RM, especially strong completeness results about it (the full proofs of which are difficult to find in the literature).