 Rantala’s approach divides the worlds into normal and non-normal ones. Normal worlds behave like possible worlds whereas at non-normal worlds, every sentence is assigned an arbitrary truth value. In effect, complex sentences \(\neg A, A \vee B\), and so on, are treated as if they were atomic sentences. The truth value of \(\neg A\) is independent of \(A\); the value of \(A \vee B\) is independent of the values of \(A\) and \(B\) at a non-normal world; and so on for the other complex sentences. These non-normal worlds are thus a very anarchic form of impossible world. Priest (2005, 2016) calls them open worlds, since they are not closed under any rule of inference (other than the trivial rule allowing one to infer \(A\) from \(A\); see also Jago 2014a).