Relevant logics for entailment have correspondences for a ternary relation $textit{R}$ such that $M,avDash (Ato B)$ just if $forall b, c(M,bvDash A Rightarrow M,cvDash B)$.

Various conditions upon $textit{R}$ correspond with, or induce axioms for $to$. Some examples are stated in the following Wikipedia article Relevance logic; as an example, $textit{R}aaa$ induces the axiom $(Awedge(Ato B))to B$.

Where may I find more correspondences, in order to identify the conditions we need upon $textit{R}$ to obtain the modal logic identified as $textit{TW}$ in (Relevance logic)?1