Qualitative and quantitative approaches to reasoning about uncertainty can lead to different logical systems for formalizing such reasoning, even when the language for expressing uncertainty is the same. In the case of reasoning about relative likelihood, with statements of the form $\varphi\succsim\psi$ expressing that $\varphi$ is at least as likely as $\psi$, a standard qualitative approach using preordered preferential structures yields a dramatically different logical system than a quantitative approach using probability measures. In fact, the standard preferential approach validates principles of reasoning that are incorrect from a probabilistic point of view. However, in this paper we show that a natural modification of the preferential approach yields exactly the same logical system as a probabilistic approach--not using single probability measures, but rather sets of probability measures. Thus, the same preferential structures used in the study of non-monotonic logics and belief revision may be used in the study of comparative probabilistic reasoning based on imprecise probabilities.

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比较概率推理的优先结构

定性和定量方法对不确定性进行推理可能会导致用于形式化这种推理的不同逻辑系统，即使表达不确定性的语言是相同的。在推理相对可能性的情况下，以$ \ varphi \ succsim \ psi $形式的语句表示$ \ varphi $的可能性至少与$ \ psi $一样，使用预定优先结构的标准定性方法会产生显着影响与使用概率测度的定量方法不同的逻辑系统。实际上，标准优先方法从概率的角度验证了不正确的推理原理。然而，在本文中，我们证明了对优惠方法的自然修改会产生与概率方法完全相同的逻辑系统-不使用单一概率测度，而是使用概率测度集。因此，用于非单调逻辑和信念修正的相同优先结构可用于基于不精​​确概率的比较概率推理的研究。