Choices rarely deal with certainties; and, where assertoric logic and modal logic are insufficient, those seeking to be reasonable turn to one or more things called “probability.” These things typically have a shared mathematical form, which is an arithmetic construct. The construct is often felt to be unsatisfactory for various reasons. A more general construct is that of a preordering, which may even be incomplete, allowing for cases in which there is no known probability relation between two propositions or between two events. Previous discussion of incomplete preorderings has been as if incidental, with researchers focusing upon preorderings for which quantifications are possible. This article presents formal axioms for the more general case. Challenges peculiar to some specific interpretations of the nature of probability are brought to light in the context of these propositions. A qualitative interpretation is offered for probability differences that are often taken to be quantified. A generalization of Bayesian updating is defended without dependence upon coherence. Qualitative hypothesis testing is offered as a possible alternative in cases for which quantitative hypothesis testing is shown to be unsuitable.

中文翻译：

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形式定性概率

选择很少涉及确定性；并且，在断言逻辑和模态逻辑不足的地方，那些寻求合理的人会转向一种或多种称为“概率”的东西。这些东西通常具有共享的数学形式，即算术构造。由于各种原因，人们常常觉得该构造不令人满意。更一般的结构是预排序结构，它甚至可能是不完整的，允许两个命题之间或两个事件之间没有已知概率关系的情况。之前对不完整预排序的讨论似乎是偶然的，研究人员专注于可以量化的预排序。本文介绍了更一般情况的形式公理。在这些命题的背景下，一些对概率性质的特定解释所特有的挑战被暴露出来。为通常被量化的概率差异提供了定性解释。贝叶斯更新的泛化在不依赖连贯性的情况下得到辩护。在定量假设检验被证明不适合的情况下，提供定性假设检验作为可能的替代方案。