Algorithms for coherence checking and propagation of conditional probability bounds

In this paper, we propose some algorithms for the checkingof generalized coherence (g-coherence) and for the extension of impreciseconditional probability assessments. Our concept of g-coherence is ageneralization of de Finetti’s coherence principle and is equivalent to the”avoiding uniform loss” property for lower and upper probabilities (a laWalley). By our algorithms we can check the g-coherence of a given impreciseassessment and we can correct it in order to obtain the associatedcoherent assessment (in the sense of Walley and Williams). Exploitingsome properties of the random gain we show how, in the linear systemsinvolved in our algorithms, we can work with a reduced set of variablesand a reduced set of linear constraints. We also show how to computesuch reduced sets. Finally, we illustrate our methods by an example relatedto probabilistic default reasoning.