In our paper “A general characterization of the variable-sharing property by means of logical matrices”, a general class of so-called “Relevant logical matrices”, RMLs, is defined. The aim of this paper is to define a class of simpler Relevant logical matrices RMLs′ serving the same purpose that RMLs, to wit: any logic verified by an RML′ has the variable-sharing property and related properties predicable of the logic of entailment E and of the logic of relevance R.
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