 The existence-conditions of a whole often depend upon facts about its parts. If there are disjunctive / conjunctive facts which contain the corresponding disjuncts / conjuncts, then any such fact exists in a world iff some disjuncts / all the conjuncts do. And if there is a negative fact containing the corresponding negated item, the former fact exists in a world iff the latter does not. These existence-conditions are written into the nature of the Boolean operations.