Bridging Jeffrey's Rule, AGM Revision and Dempster Conditioning in the Theory of Evidence
Bridging Jeffrey's Rule, AGM Revision and Dempster Conditioning in the Theory of Evidence
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DOI：
10.1142/s0218213011000401
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发表时间：
2011-08
期刊：
影响因子：
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通讯作者：
Jianbing Ma;Weiru Liu;D. Dubois;H. Prade
中科院分区：
文献类型：
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作者：
Jianbing Ma;Weiru Liu;D. Dubois;H. Prade
信念修正是指在收到新证据时修正代理人信念的过程。在人工智能领域，修正策略在基于逻辑的形式主义和概率运动学的背景下得到了广泛的研究。然而，迄今为止，证据理论中关于这一主题的文献并不多。相比之下，证据理论中迄今为止提出的组合规则，特别是登普斯特规则，是对称的。它们依赖于一个基本假设，即组合在一起的证据被认为是同等的，即发挥相同的作用。当一种证据来源不如另一种证据来源可靠时，可以对其进行折扣，然后仍然使用对称组合运算。在修订的情况下，其想法是让代理的先验知识被一些输入信息改变。因此，变革问题本质上是不对称的。假设输入信息是可靠的，则应保留该信息，同时应尽量减少对先前信息的更改。为了解决这个问题，本文定义了证据理论修正的概念，将概率论和逻辑论的观点结合起来。回顾了之前提出的几条修订规则，我们提倡其中一条更符合修订的想法。它被扩展以处理先验信息和输入信息之间的不一致。当输入与先验信念函数强一致时，它简化为登普斯特组合规则，就像 Alchourron、Gardenfors 和 Makinson (AGM) 意义上的修正简化为扩展一样。还研究了该修订规则的属性，并证明它概括了杰弗里更新规则、登普斯特调节规则和年度股东大会修订的形式。
Belief revision characterizes the process of revising an agent's beliefs when receiving new evidence. In the field of artificial intelligence, revision strategies have been extensively studied in the context of logic-based formalisms and probability kinematics. However, so far there is not much literature on this topic in evidence theory. In contrast, combination rules proposed so far in the theory of evidence, especially Dempster rule, are symmetric. They rely on a basic assumption, that is, pieces of evidence being combined are considered to be on a par, i.e. play the same role. When one source of evidence is less reliable than another, it is possible to discount it and then a symmetric combination operation is still used. In the case of revision, the idea is to let prior knowledge of an agent be altered by some input information. The change problem is thus intrinsically asymmetric. Assuming the input information is reliable, it should be retained whilst the prior information should be changed minimally to that effect. To deal with this issue, this paper defines the notion of revision for the theory of evidence in such a way as to bring together probabilistic and logical views. Several revision rules previously proposed are reviewed and we advocate one of them as better corresponding to the idea of revision. It is extended to cope with inconsistency between prior and input information. It reduces to Dempster rule of combination, just like revision in the sense of Alchourron, Gardenfors, and Makinson (AGM) reduces to expansion, when the input is strongly consistent with the prior belief function. Properties of this revision rule are also investigated and it is shown to generalize Jeffrey's rule of updating, Dempster rule of conditioning and a form of AGM revision.