 Belief revision  is the study of rationally revising bodies of belief in the light of new evidence. Notoriously, people have inconsistent beliefs. They may even be rational in doing so. For example, there may be apparently overwhelming evidence for both something and its negation. There may even be cases where it is in principle impossible to eliminate such inconsistency. For example, consider the ‘paradox of the preface’. A rational person, after thorough research, writes a book in which they claim \(A_1\),…, \(A_n\). But they are also aware that no book of any complexity contains only truths. So they rationally believe \(\neg(A_1 \wedge \ldots \wedge A_n)\) too. Hence, principles of rational belief revision must work on inconsistent sets of beliefs. Standard accounts of belief revision, e.g. the AGM theory (see  the logic of belief revision),  all fail to do this, since they are based on classical logic (Tanaka 2005). A more adequate account may be based on a paraconsistent logic; see Girard and Tanaka 2016.