 Adding appropriate constraints provides this negation with many intuitive inferential features. If \(w^{**} = w\) for all worlds \(w\), for example, Double Negation introduction and elimination is valid. This is often called De Morgan negation, for De Morgan’s Laws hold of it. But it does not validate the Law of Explosion (that a contradiction entails any sentence). For a counterexample, take a model where \(A\) holds at \(w, B\) doesn’t hold at \(w\), and \(A\) doesn’t hold at \(w^*\). Then, both \(A\) and \(\neg A\) hold at \(w\), whereas \(B\) doesn’t: \(w\) is an inconsistent but non-trivial world.