 If the compatibility relation is not assumed to be symmetric (although it may be argued that compatibility between states is a symmetrical relation), then one may distinguish between two negation operations \(\osim _1\) and \(\osim _2\) such that that \(\osim _1 A\) is true at a state \(w\) just in case \(A\) fails to be true at every state compatible with \(w\), and \(\osim _2 A\) is true at a state \(w\) just in case \(A\) fails to be true at every state \(w\) is compatible with: