Algorithms for coherence checking and propagation of conditional probability bounds

In this paper, we propose some algorithms for the checking of generalized coherence (g-coherence) and for the extension of imprecise conditional probability assessments. Our concept of g-coherence is a generalization of de Finetti’s coherence principle and is equivalent to the ”avoiding uniform loss” property for lower and upper probabilities (a la Walley). By our algorithms we can check the g-coherence of a given imprecise assessment and we can correct it in order to obtain the associated coherent assessment (in the sense of Walley and Williams). Exploiting some properties of the random gain we show how, in the linear systems involved in our algorithms, we can work with a reduced set of variables and a reduced set of linear constraints. We also show how to compute such reduced sets. Finally, we illustrate our methods by an example related to probabilistic default reasoning.