The classically based AGM theory of belief revision takes consistency and conservativeness to be the driving forces of belief revision: When integrating new information, we attempt to maintain a consistent belief set and to do so we sometimes have to relinquish those beliefs that are relatively less entrenched. Strong paraconsistentists hold that we should abandon the consistency constraint. But what should replace it? I present a theory in which an agent's epistemic attitude towards the world is represented by a set of propositions that she believes and a set of propositions that she denies. On this view, consistency is replaced with a weaker notion of quasi-consistency -- the sets of beliefs and denials cannot overlap one another. The details of the resulting theory are explained and we will discuss the nature of the revision, contraction and expansion operators of the theory.