  The three place relation \(R\) follows closely the behaviour of the mode of premise combination in the proof theory for a substructural logic. For different logics, different conditions can be placed on \(R\). For example, if premise combination is commutative, we place a symmetry condition on \(R\) like this: \(Rxyz\) if and only if \(Ryxz\). Ternary relational semantics gives us great facility to model the behaviour of substructural logics. (The extent of the correspondence between the proof theory and algebra of substructural logics and the semantics is charted in Dunn’s work on Gaggle Theory (1991) and is summarised in Restall’s Introduction to Substructural Logics (2000).)