This is an initial systematic study of the properties of negation from the point of view of abstract deductive systems. I will start the ball rolling by discussing the unifying representational formalism adopted, which involves multiple-consequence relations. I will then concentrate on what negation can be, showing the interrelations among a great number of positive contextual sub-classical properties of negation. All properties are important, but some are more important than others: I will argue next that more attention should be paid to negative properties in the specification of what a logic or a logical constant is.