 As a consequence, the combined logic of negation and disjunction (which can be defined as the logic over \(\neg\) and \(\vee\) characterized by the valuations over \(\{0,1\}\) satisfying both clauses above) validates \((\varphi \vee \neg \varphi)\), and so classical logic is recovered. This is the result obtained by the combination method called direct union of matrices, introduced in Coniglio and Fernández 2005. However, if algebraic fibring is considered in categories such as those of Hilbert calculi or consequence relations, the combination between the logic of negation and the logic of disjunction results in a logic defined over \(\neg\) and \(\vee\) which is weaker than classical logic: the interaction law \((\varphi \vee \neg \varphi)\) is no longer valid. That is, an arguably desirable interaction between the connectives is lost in the combination process, and classical logic expressed over \(\neg\) and \(\vee\) cannot be recovered from its fragments, as long as algebraic fibring in these categories of logics is used.