 (C1), often dubbed Closure under entailment or Full omniscience, has it that one knows or believes all the logical consequences of what one knows or believes. (C2), Knowledge of all validities or Belief in all validities, has it that one knows or believes all logical truths. (C3) ensures the consistency of knowledge or belief. All follow from understanding \(K\) as a quantifier over worlds, as per (H). (C1): if \(A\)’s entailing \(B\) is understood in terms of all \(A\)-worlds’ being \(B\)-worlds (in all the relevant models), and given that \(KA\) means that \(A\) is true at all the epistemically accessible worlds, \(B\) will be true there, too, and so \(KB\) will hold. (C2): if \(A\)’s being logically valid is understood as its holding at all worlds (of all the relevant models), then it will hold at all the epistemically accessible ones, and so \(KA\) will hold. (C3): no possible world, thus no accessible one, will make both \(A\) and \({\sim}A\) true.