Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Revision rules for convex sets of probabilities
Mathematical models for handling partial knowledge in artificial intelligence
Artificial Intelligence
Semigraphoids and structures of probabilistic conditional independence
Annals of Mathematics and Artificial Intelligence
Strong Conditional Independence for Credal Sets
Annals of Mathematics and Artificial Intelligence
On separation criterion and recovery algorithm for chain graphs
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
A survey of the theory of coherent lower previsions
International Journal of Approximate Reasoning
Probabilistic logic with independence
International Journal of Approximate Reasoning
Imprecise markov chains and their limit behavior
Probability in the Engineering and Informational Sciences
Epistemic irrelevance in credal nets: The case of imprecise Markov trees
International Journal of Approximate Reasoning
Artificial Intelligence
Notes on desirability and conditional lower previsions
Annals of Mathematics and Artificial Intelligence
Exchangeability and sets of desirable gambles
International Journal of Approximate Reasoning
Irrelevant and independent natural extension for sets of desirable gambles
Journal of Artificial Intelligence Research
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This paper studies graphoid properties for epistemic irrelevance in sets of desirable gambles. For that aim, the basic operations of conditioning and marginalization are expressed in terms of variables. Then, it is shown that epistemic irrelevance is an asymmetric graphoid. The intersection property is verified in probability theory when the global probability distribution is positive in all the values. Here it is always verified due to the handling of zero probabilities in sets of gambles. An asymmetrical D-separation principle is also presented, by which this type of independence relationships can be represented in directed acyclic graphs.