 If we define validity in terms of truth preservation under all relational evaluations then we obtain First Degree Entailment (FDE) which is a fragment of relevant logics. These relational semantics for FDE are due to Dunn 1976; cf. Omori and Wansing 2017. A different approach is explored through the idea of non-deterministic matrices, studied by Avron and his collaborators (for example, Avron &amp; Lev 2005).