现实与概率：介绍一种新的概率演算
Reality and Probability: Introducing a New Type of Probability Calculus
摘要：
我们考虑一个现实的概念是这样的：一个对象是“真实的”，如果我们知道，如果我们试图测试这个对象是否存在，这个测试会给我们肯定的答案“是”。如果我们考虑一个概率起着基本作用的实在概念，就可以表明，标准概率论不太适合用“概率等于1”来代替“确定性”。对这个问题的分析使我们提出了一种新的概率论，它是标准概率论的推广。这种新类型的概率是区间[0，1]的所有子集的集合的函数，而不是区间[0，1]本身，因此它的评估是通过子集而不是数字来进行的。这个子集对应于相对频率序列的不同限制，当考虑到在实验过程中对背景以及它如何影响所研究的物理实体的状态的内在缺乏知识时，可能会出现这种限制。新的概率论使得在日内瓦-布鲁塞尔量子力学方法中定义一整套实验的概率成为可能，这在标准概率论中是不可能的。本文介绍了一种“状态实验概率系统”的结构，并导出了作为这种结构特例的状态属性系统。状态实验概率系统及其态射范畴SEP与状态属性系统及其态射范畴SP是联系在一起的
英文摘要：
We consider a conception of reality that is the following: An object is 'real' if we know that if we would try to test whether this object is present, this test would give us the answer 'yes' with certainty. If we consider a conception of reality where probability plays a fundamental role it can be shown that standard probability theory is not well suited to substitute 'certainty' by means of 'probability equal to 1'. The analysis of this problem leads us to propose a new type of probability theory that is a generalization of standard probability theory. This new type of probability is a function to the set of all subsets of the interval [0, 1] instead of to the interval [0, 1] itself, and hence its evaluation happens by means of a subset instead of a number. This subset corresponds to the different limits of sequences of relative frequency that can arise when an intrinsic lack of knowledge about the context and how it influences the state of the physical entity under study in the process of experimentation is taken into account. The new probability theory makes it possible to define probability on the whole set of experiments within the Geneva-Brussels approach to quantum mechanics, which was not possible with standard probability theory. We introduce the structure of a 'state experiment probability system' and derive the state property system as a special case of this structure. The category SEP of state experiment probability systems and their morphisms is linked with the category SP of state property systems and their morphisms
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