A framework for managing uncertain inputs: An axiomization of rewarding
A framework for managing uncertain inputs: An axiomization of rewarding
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DOI：
10.1016/j.ijar.2011.05.004
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发表时间：
2011-10
期刊：
影响因子：
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通讯作者：
Jianbing Ma;Weiru Liu
中科院分区：
文献类型：
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作者：
Jianbing Ma;Weiru Liu
信念修正中的成功假设确保了新的证据（输入）总是可信的。然而，承认不确定输入受到了许多研究人员的质疑。达尔文和珀尔认为，应该引入证据的力量来确定信念变化的结果，并对这一思想提供了初步的定义。在本文中，我们从Darwiche和Pearl的想法开始，旨在开发一个框架，可以通过一些合理的假设来捕捉输入强度的影响。为了实现这一目标，我们首先定义认知状态来表示带有强度的信念，然后提出一组假设来描述由输入强度决定的认知状态的变化过程，并建立表征定理来表征这些假设。结果，我们得到了一个唯一的奖励算子，该算子被证明是一个与许多其他工作一致的合并算子。我们还研究了现有的关于信念合并的公设，并与我们的公设进行了比较。此外，我们还证明了从一个认知状态可以推导出一个对应的Spohn有序条件函数，从而将两个认知状态的组合结果简化为Laverny和Lang提出的两个对应的有序条件函数的组合结果。进一步，当我们简化到信念修正情形时，我们证明了我们的结果可以推导出达尔文和珀尔的所有公设，以及顽抗公设和独立公设。
The success postulate in belief revision ensures that new evidence (input) is always trusted. However, admitting uncertain input has been questioned by many researchers. Darwiche and Pearl argued that strengths of evidence should be introduced to determine the outcome of belief change, and provided a preliminary definition towards this thought. In this paper, we start with Darwiche and Pearl’s idea aiming to develop a framework that can capture the influence of the strengths of inputs with some rational assumptions. To achieve this, we first define epistemic states to represent beliefs attached with strength, and then present a set of postulates to describe the change process on epistemic states that is determined by the strengths of input and establish representation theorems to characterize these postulates. As a result, we obtain a unique rewarding operator which is proved to be a merging operator that is in line with many other works. We also investigate existing postulates on belief merging and compare them with our postulates. In addition, we show that from an epistemic state, a corresponding ordinal conditional function by Spohn can be derived and the result of combining two epistemic states is thus reduced to the result of combining two corresponding ordinal conditional functions proposed by Laverny and Lang. Furthermore, when reduced to the belief revision situation, we prove that our results induce all the Darwiche and Pearl’s postulates as well as the Recalcitrance postulate and the Independence postulate.