 In order to get rid of such entailments as \(A \rightarrow  (B \rightarrow B)\), we need some world at which \(A\) holds but \(B \rightarrow B\) fails. One way to achieve this may be to admit “partial” or incomplete situations of the kind studied in  situation semantics,  at which \(A\) holds but \(B \rightarrow B\) fails to hold, just because they carry no information about \(B\). Another way is via impossible worlds: an understanding of such worlds, as we have seen, is as scenarios where logical laws may fail, and the Law of (propositional) Identity, stating that any formula entails itself, is one of them. At possible worlds, we still require for the truth of conditionals \(A \rightarrow B\) that at every accessible world where \(A\) holds, \(B\) holds, too. Consequently, \(A \rightarrow(B \rightarrow B)\) is not logically valid. Technically, when \(w\) is an impossible world, we state the truth conditions for the conditional, by means of the ternary \(R\), as follows: