Abstract

Routley-Meyer ternary relational semantics was introduced in the early seventies of the past century. RM-semantics was intended to model classical relevant logics such as the logic of the relevant conditional R and the logic of Entailment E. But, ever since Routley and Meyer’s first papers on the topic, this essentially malleable semantics has been used for characterizing more general relevant logics or even non-relevant logics. The aim of this paper is to provide an RM-semantics with respect to which Łukasiewicz 3-valued logic Ł3 is sound and complete. Ł3 is understood as the set of all valid formulas in Łukasiewicz 3-valued matrices MŁ3. In this sense, leaning on previous work by us, Ł3 is axiomatized as an extension of Routley and Meyer’s basic positive logic B+, labelled Ł3. And the RM-semantics for Ł3 is actually defined for this particular axiomatization of Ł3. The result presented in the paper is interesting from the Universal Logic perspective, in the sense that it connects Łukasiewicz many-valued logics and similar systems to relevant logics from the point of view of the latter, the 3-termed relational point of view, in particular.