 What is the intuitive connection between \(w\) and \(w^*\)? The idea is that the twins are “mirror images one of the other reversing ‘in’ and ‘out’” (Dunn 1986: 191). If \(w\) is \(A\)-inconsistent (both \(A\) and \(\neg A\) hold), then \(w^*\) is \(A\)-incomplete (neither \(A\) nor \(\neg A\) hold), and vice versa. The \({}^*\) takes local inconsistency into local incompleteness and vice versa. It may also be the case that \(w = w^*\): the twins are in fact one. In that case, \(w\) must be a maximal and consistent world, where negation behaves classically: \(\neg A\) is true if and only if \(A\) is false there.