 It is possible to make the connection between belief revision and nonmonotonic logic precise. Given a belief set \(\bB\) and a revision operation \(*,\) we can define a defeasible consequence relation by setting \(\alpha \dproves \beta \text{ iff } \beta \in \bB*\alpha.\) Similarly, given a defeasible consequence relation \(\dproves\) we can define \(\bB = \{ \alpha : \top \dproves \alpha \} \text{ and } \bB * \alpha = \{ \beta : \alpha\dproves \beta \}.\) Then it is possible to prove the following correspondences between AGM belief revision and the set of principles we called System R in  Section 2.1.1.  It follows that AGM revision can be represented in terms of a total preferential model over possible worlds.