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 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. It is also presented an asymmetrical D-separation principle, by which this type of independence relationships can be represented in directed acyclic graphs.
Keywords. Sets of desirable gambles, epistemic irrelevance, graphoid axioms, natural extension
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Dpto. Ciencias de la Computación e IA
Universidad de Granada
18071 Granada - Spain