 The key difference between \((\rightarrow)\) and the standard modal clause for the strict conditional (which is true at a world if and only if, at all accessible worlds where the antecedent is true, the consequent is true), is that the worlds of the antecedent and the consequent have been “split”. Specifically, \(B \rightarrow B\) fails at impossible worlds \(w\) when there are worlds \(w_1\) and \(w_2\) such that R\(ww_1 w_2, B\) holds at the former, but fails at the latter. Since we do not want \(B \rightarrow B\) to fail at normal/possible worlds, we can add a Normality Condition, saying that the accessible worlds \(w_1\) and \(w_2\) are one and the same: