 This approximately Carnapian concern with sequent-definability—in particular the exclusion of unwanted non-Boolean valuations—can be taken to a higher level by moving from questions about sequents and the valuations they hold, to questions about rules and the valuations they preserve the property of holding on, as we shall see in Section  3,  after making some further points about the apparatus of consequence relations, or logics in the framework Set-Fmla. The determinant-induced conditions on generalized consequence relations alluded to above can be converted into conditions on consequence relations in a straightforward way, illustrated here in the case of negation, with the condition