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.
翻译:在本文中,我们表明,一系列连贯的赌博和一致的下层和上层观点可以嵌入信息代数的代数结构中,这首先导致对可取性和不精确概率的代数和逻辑结构的新认识,其次,它将不精确的概率与共享相同基本结构的计算机科学中的其他形式主义联系起来,在考虑产品可能性空间的情况下,提出了无域和对由此产生的信息代数的标签式观点。此外,还表明两者都是非原子学的,因此可以嵌入定代数中。