具有上下概率的独立性
Independence with Lower and Upper Probabilities
摘要：
结果表明，区间概率表示捕捉认识论的独立性的能力是非常有限的。如果对第一个事件的知识不改变信念，那么两个事件在认识论上是独立的（即，概率边界）。然而，这种形式的独立性只能存在于退化情况下的2-单调概率函数中，即，前提是先验界要么是点概率要么是完全空的其他类别的低概率也有额外的限制。有人认为，这些现象只是一个解释的问题。当人们将概率界限解释为认识论不确定性的度量时，它们似乎是限制（即，由于缺乏知识而产生的不确定性），但是当概率区间被解释为本体论不确定性（由结构近似引入的不确定性）的表示时，人们会完全期望。本体论的解释进行了介绍和讨论。
英文摘要：
It is shown that the ability of the interval probability representation to capture epistemological independence is severely limited. Two events are epistemologically independent if knowledge of the first event does not alter belief (i.e., probability bounds) about the second. However, independence in this form can only exist in a 2-monotone probability function in degenerate cases i.e., if the prior bounds are either point probabilities or entirely vacuous. Additional limitations are characterized for other classes of lower probabilities as well. It is argued that these phenomena are simply a matter of interpretation. They appear to be limitations when one interprets probability bounds as a measure of epistemological indeterminacy (i.e., uncertainty arising from a lack of knowledge), but are exactly as one would expect when probability intervals are interpreted as representations of ontological indeterminacy (indeterminacy introduced by structural approximations). The ontological interpretation is introduced and discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
