  One might assume from this discussion that \(\bK\) is the correct logic when \(\Box\) is read ‘it will always be the case that’. However, there are reasons for thinking that \(\bK\) is too weak. One obvious logical feature of the relation \(R\) (earlier than) is transitivity. If \(wRv (w\) is earlier than \(v)\) and \(vRu (v\) is earlier than \(u)\), then it follows that \(wRu (w\) is earlier than \(u)\). So let us define a new kind of validity that corresponds to this condition on \(R\). Let a 4-model be any model whose frame \(\langle W, R\rangle\) is such that \(R\) is a transitive relation on \(W\). Then an argument is 4-valid iff any 4-model whose valuation assigns \(T\) to the premises at a world also assigns \(T\) to the conclusion at the same world. We use ‘4’ to describe such a transitive model because the logic which is adequate (both sound and complete) for 4-validity is \(\mathbf{K4}\), the logic which results from adding the axiom (4): \(\Box A\rightarrow \Box \Box A\) to \(\bK\).