Editing Belief revision (section)

==Non-monotonic inference relation==
Given a fixed knowledge base <math>K</math> and a revision operator <math>*</math>, one can define a non-monotonic inference relation using the following definition: <math>P \vdash Q</math> if and only if <math>K*P \models Q</math>. In other words, a formula <math>P</math> [[logical consequence|entails]] another formula <math>Q</math> if the addition of the first formula to the current knowledge base leads to the derivation of <math>Q</math>. This inference relation is non-monotonic.

The AGM postulates can be translated into a set of postulates for this inference relation. Each of these postulates is entailed by some previously considered set of postulates for non-monotonic inference relations. Vice versa, conditions that have been considered for non-monotonic inference relations can be translated into postulates for a revision operator. All these postulates are entailed by the AGM postulates.