Abstract This paper introduces and investigates Depth-bounded Belief functions, a logic-based representation of quantified uncertainty. Depth-bounded Belief functions are based on the framework of Depth-bounded Boolean logics [4] , which provide a hierarchy of approximations to classical logic. Similarly, Depth-bounded Belief functions give rise to a hierarchy of increasingly tighter lower and upper bounds over classical measures of uncertainty. This has the rather welcome consequence that “higher logical abilities” lead to sharper uncertainty quantification. In particular, our main results identify the conditions under which Dempster-Shafer Belief functions and probability functions can be represented as a limit of a suitable sequence of Depth-bounded Belief functions.

中文翻译：

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深度有界的信念函数

摘要 本文介绍并研究了深度有界置信函数，这是一种基于逻辑的量化不确定性表示。深度有界信念函数基于深度有界布尔逻辑 [4] 的框架，它提供了经典逻辑的近似层次结构。类似地，深度有界置信函数产生了一个层次结构，该层次结构的下限和上限比经典的不确定性度量更严格。这具有相当受欢迎的结果，即“更高的逻辑能力”导致更清晰的不确定性量化。特别是，我们的主要结果确定了可以将 Dempster-Shafer 置信函数和概率函数表示为合适的深度有界置信函数序列的限制的条件。