Non-monotonic Inference Relation
Given a fixed knowledge base and a revision operator, one can define a non-monotonic inference relation using the following definition: if and only if . In other words, a formula entails another formula if the addition of the first formula to the current knowledge base leads to the derivation of . 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.
Read more about this topic: Belief Revision
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