Artificial Intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Locally Strong Coherence in Inference Processes
Annals of Mathematics and Artificial Intelligence
Strong Conditional Independence for Credal Sets
Annals of Mathematics and Artificial Intelligence
Computing probability intervals under independency constraints
UAI '90 Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence
Separation Properties of Sets of Probability Measures
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
An Investigation of the Laws of Thought
An Investigation of the Laws of Thought
Probabilistic logic under coherence: complexity and algorithms
Annals of Mathematics and Artificial Intelligence
Notes on conditional previsions
International Journal of Approximate Reasoning
Marginal extension in the theory of coherent lower previsions
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Updating coherent previsions on finite spaces
Fuzzy Sets and Systems
International Journal of Approximate Reasoning
Conservative inference rule for uncertain reasoning under incompleteness
Journal of Artificial Intelligence Research
Epistemic irrelevance in credal nets: The case of imprecise Markov trees
International Journal of Approximate Reasoning
Artificial Intelligence
Conglomerable natural extension
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
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We study the consistency of a number of probability distributions, which are allowed to be imprecise. To make the treatment as general as possible, we represent those probabilistic assessments as a collection of conditional lower previsions. The problem then becomes proving Walley's (strong) coherence of the assessments. In order to maintain generality in the analysis, we assume to be given nearly no information about the numbers that make up the lower previsions in the collection. Under this condition, we investigate the extent to which the above global task can be decomposed into simpler and more local ones. This is done by introducing a graphical representation of the conditional lower previsions that we call the coherence graph: we show that the coherence graph allows one to isolate some subsets of the collection whose coherence is sufficient for the coherence of all the assessments; and we provide a polynomial-time algorithm that finds the subsets efficiently. We show some of the implications of our results by focusing on three models and problems: Bayesian and credal networks, of which we prove coherence; the compatibility problem, for which we provide an optimal graphical decomposition; probabilistic satisfiability, of which we show that some intractable instances can instead be solved efficiently by exploiting coherence graphs.