 Even though we have ignored the non-normal worlds in this definition, they still play a role in invalidating Necessitation. For take any classical propositional tautology, say \(A \vee \neg A\). This holds at all worlds of all models, so \(\Box(A \vee \neg A)\) holds at all normal worlds and hence is valid. But \(\Box(A \vee \neg A)\) holds at no non-normal world. Now suppose \(w\) is a normal world that has access to any non-normal world. Then \(\Box \Box(A \vee \neg A)\) is false at \(w\) and so (since \(w\) is normal) \(\Box \Box(A \vee \neg A)\) is not valid. That’s a counterexample to Necessitation.