论文标题
关于数字事件的布尔式
On Boolean posets of numerical events
论文作者
论文摘要
令S为物理系统的一组状态，P（s）当系统处于状态s时发生事件的可能性。从s到[0,1]的函数p称为数值事件，或者称为s-探行性。如果通过真实功能的顺序排序S频率的一组P，则可以将其视为量子逻辑。如果p是布尔代数，这将表明潜在的物理系统是经典的系统。本文的目的是研究S型探索性的集合，这些探索与布尔代数相距不远，尤其是通过对这些集合中发生的函数的添加和比较进行比较。特别是，某些类别的s-探针的布尔值是特征性的，并且相互关联，并基于状态集的描述得出。
Let S be a set of states of a physical system and p(s) the probability of the occurrence of an event when the system is in state s. A function p from S to [0,1] is called a numerical event or alternatively, an S-probability. If a set P of S-probabilities is ordered by the order of real functions it becomes a poset which can be considered as a quantum logic. In case P is a Boolean algebra this will indicate that the underlying physical system is a classical one. The goal of this paper is to study sets of S-probabilities which are not far from being Boolean algebras, especially by means of the addition and comparison of functions that occur in these sets. In particular, certain classes of Boolean posets of S-probabilities are characterized and related to each other and descriptions based on sets of states are derived.
