The Systems of Relevance Logic
The Systems of Relevance Logic

Summary/Abstract: The system R, or more precisely the pure implicational fragment R ->, is considered by the relevance logicians as the most important. Another central system of relevance logic hasbeen 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 twoapproaches 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 charactirized only by rules of deducibility.

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