 Logical consequence and validity are defined with respect to possible (normal) worlds only. Impossible worlds come into play only when evaluating knowledge claims, \(KA\). So, ignoring \(K\)-sentences, the logic is classical. But the logic of \(K\)-sentences is not closed under any non-trivial rule of inference, thereby dispensing with Closure, Validity, and (in the case of belief) Consistency. An agent is modelled as having inconsistent beliefs, for example, simply by treating an impossible world where both \(A\) and \(\neg A\) are true as being epistemically accessible (from the actual world) for that agent.