We examine several concepts of independence associated with (1) credal sets, understood as sets of probability measures, (2) sets of full conditional probabilities, (3) sets of lexicographic probabilities, and (4) sets of desirable gambles. Concepts of independence are evaluated with respect to the graphoid properties they satisfy, as these properties capture important abstract features of “independence”. We emphasize the analysis of sets of probability measures as this is a popular formalism, looking at versions of epistemic, confirmational, and type-5 independence that are based on regular conditioning, as well as complete and strong independence. We then examine analogous concepts of independence for sets of full conditional probabilities, sets of lexicographic probabilities, and sets of desirable gambles.

我们研究了与（1）crecre集，被理解为概率测度集，（2）完全条件概率集，（3）lexicographic概率集和（4）期望赌博集相关的几个独立性概念。关于独立性的概念，要根据它们满足的石墨特性进行评估，因为这些特性捕获了“独立性”的重要抽象特征。我们强调对概率测度集的分析，因为这是一种流行的形式主义，着眼于基于常规条件的认知，确认和5型独立性以及完全独立和强烈独立性的版本。然后，我们检查完全条件概率集，词典概率集和期望赌博集的独立性的类似概念。