The quasi-relevant 3-valued logic RM3 and some of its sublogics lacking the variable-sharing property
The quasi-relevant 3-valued logic RM3 and some of its sublogics lacking the variable-sharing property

Summary/Abstract: The logic RM3 is the 3-valued extension of the logic R-Mingle (RM). RM (and so, RM3) does not have the variable- sharing property (vsp), but RM3 (and so, RM) lacks the more oending" paradoxes of relevance", such as A → (B → A) or A → (A → B). Thus, RM and RM3 can be useful when some relevance", but not the full vsp, is needed. Sublogics of RM3 with the vsp are well known, but this is not the case with those lacking this property. The rst aim of this paper is to dene an ample family of sublogics of RM3 without the vsp. The second one is to provide these sublogics and RM3 itself with a general Routley- Meyer semantics, that is, the semantics devised for relevant logics in the early seventies of the past century.

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