The Systems of Relevance Logic

Abstract

The system R, or more precisely the pure implicational fragment R→, is considered by the relevance logicians as the most important. The another central system of relevance logic has been the logic E of entailment that was supposed to capture strict relevant implication. The next system of relevance logic is RM or R-mingle. The question is whether adding mingle axiom to R→ yields the pure implicational fragment RM→ of the system? As concerns the weak systems there are at least two approaches to the problem. First of all, it is possible to restrict a validity of some theorems. In another approach we can investigate even weaker logics which have no theorems and are characterized only by rules of deducibility.