论文标题
可能性和概率的解释
An exposition of possibility and probability
论文作者
论文摘要
本文考虑了可能事件的概念，这些事件在概率分析中无关紧要（即，概率为零的事件）。本文根据“可能的世界”讨论了模态逻辑的方法，并讨论了有时（错误地）被认为是根据概率定义的可能性，不可能和确定性概念的数学框架。对于一般概率空间和这些空间的改进，探索了可能性和概率之间的关系，在其他事件上有条件，特别关注事件概率为零的属性。我们得出了条件，在某些情况下，可能性和意义分歧和条件可以与等效思想进行调和。我们还将此分析应用于多项式模型中的可能性和概率问题。
This paper considers the notion of possible events which are insignificant in probabilistic analysis (i.e. events that have zero probability). The paper discusses the method of modal logic based on "possible worlds" and discusses a mathematical framework for the concepts of possibility, impossibility and certainty that are sometimes (incorrectly) thought to be defined with respect to probability. The relationship between possibility and probability is explored for general probability spaces and for refinements of these spaces conditional on other events, with particular focus on the properties of events having zero probability. We derive conditions under which possibility and significance diverge and conditions under which they can be reconciled as equivalent ideas within certain contexts. We also apply this analysis to discuss issues in possibility and probability in the multinomial model.
