不精确概率论中的信息代数
Information algebras in the theory of imprecise probabilities
摘要：
在本文中，我们表明，相干集的赌博和相干的上下预测可以嵌入到信息代数的代数结构。这导致首先，一个新的角度的代数和逻辑结构的愿望和不精确的概率，其次，它连接不精确的概率，以其他形式主义在计算机科学共享相同的基本结构。考虑乘积可能性空间，给出了所得信息代数的自由域和标号视图。此外，它表明，两者都是原子的，因此它们可以嵌入到集合代数。
英文摘要：
In this paper, we show that coherent sets of gambles and coherent lower and upper previsions can be embedded into the algebraic structure of information algebra. This leads firstly, to a new perspective of the algebraic and logical structure of desirability and imprecise probabilities and secondly, it connects imprecise probabilities to other formalism in computer science sharing the same underlying structure. Both the domain free and the labeled view of the resulting information algebras are presented, considering product possibility spaces. Moreover, it is shown that both are atomistic and therefore they can be embedded in set algebras.
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。
