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
Famous quotes containing the words inference and/or relation:
“I have heard that whoever loves is in no condition old. I have heard that whenever the name of man is spoken, the doctrine of immortality is announced; it cleaves to his constitution. The mode of it baffles our wit, and no whisper comes to us from the other side. But the inference from the working of intellect, hiving knowledge, hiving skill,—at the end of life just ready to be born,—affirms the inspirations of affection and of the moral sentiment.”
—Ralph Waldo Emerson (1803–1882)
“Whoever has a keen eye for profits, is blind in relation to his craft.”
—Sophocles (497–406/5 B.C.)