Probabilistic models and graph-based independence languages have often been combined in artificial intelligence research. The Bayesian network formalism is probably the best example of this type of association. In this article we focus on graphical structures that associate graphs with sets of probability measures ― the result is referred to as a credal network. We describe credal networks and review an algorithm for evidential reasoning that we have recently developed. The algorithm substantially simplifies the computation of upper and lower probabilities by exploiting an independence assumption (strong independence) and a representation based on separately specified sets of probability measures. The algorithm is particularly efficient when applied to poly-tree structures. We then discuss a strategy for approximate reasoning in multi-connected networks, based on conditioning.
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