 Like the semantics of modal logic, the semantics of relevance logic relativises truth of formulae to worlds. But Routley and Meyer go modal logic one better and use a three-place relation on worlds. This allows there to be worlds at which \(q \rightarrow q\) fails and that in turn allows worlds at which \(p \rightarrow(q \rightarrow q)\) fails. Their truth condition for \(\rightarrow\) on this semantics is the following: