摘要翻译：
本文提出了一种概率论(SP)符号推广的决策理论。Darwiche和Ginsberg[2,3]提出了SP，在保留贝叶斯推理的理想模式的同时，放松了对不确定性使用数字的要求。SP通过符号支持来表示不确定性，符号支持是部分有序的，而不是像标准概率那样完全有序的。我们证明了在满足许多直觉公设的行为上的偏好关系是由一个效用函数表示的，该效用函数的定义域是一组支持对。我们认为主观解释对于SP和对于数值概率一样有用和合适。它是有用的，因为主观解释为不确定性引出提供了基础。这是恰当的，因为我们可以提供一个决策理论来解释对行为的偏好是如何基于支持比较的。
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英文标题：
《Decision Making for Symbolic Probability》
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作者：
Phan H. Giang, Sathyakama Sandilya
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最新提交年份：
2012
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Artificial Intelligence        人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
  This paper proposes a decision theory for a symbolic generalization of probability theory (SP). Darwiche and Ginsberg [2,3] proposed SP to relax the requirement of using numbers for uncertainty while preserving desirable patterns of Bayesian reasoning. SP represents uncertainty by symbolic supports that are ordered partially rather than completely as in the case of standard probability. We show that a preference relation on acts that satisfies a number of intuitive postulates is represented by a utility function whose domain is a set of pairs of supports. We argue that a subjective interpretation is as useful and appropriate for SP as it is for numerical probability. It is useful because the subjective interpretation provides a basis for uncertainty elicitation. It is appropriate because we can provide a decision theory that explains how preference on acts is based on support comparison.
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PDF链接：
https://arxiv.org/pdf/1207.4111