 Semantics for the relevant conditional are obtained by furnishing each Routley-Meyer model with a ternary relation. In the simplified semantics of Priest and Sylvan (1992) and Restall (1993, 1995), worlds are divided into normal and non-normal. If \(w\) is a normal world, \(A \rightarrow B\) is true at \(w\) iff at all worlds where \(A\) is true, \(B\) is true. If \(w\) is non-normal, \(A \rightarrow B\) is true at \(w\) iff for all \(x, y\), such that \(Rwxy\), if \(A\) is true at \(x, B\) is true at \(y\). If \(B\) is true at \(x\) but not at \(y\) where \(Rwxy\), then \(B \rightarrow B\) is not true at \(w\). Then one can show that \(A \rightarrow (B \rightarrow B)\) is not a logical truth. (Validity is defined as truth preservation over normal worlds.) This gives the basic relevant logic, \(B\). Stronger logics, such as the logic \(R\), are obtained by adding constraints on the ternary relation.