M. Studeny: Conditional independence and natural conditional functions. International Journal of Approximate Reasoning 12 (1995), n. 1, pp. 43-68.

The concept of conditional independence within the framework of Spohn's theory of natural conditional functions is studied. Basic properties of conditional independence within this framework are recalled and further results analogical to the results concerning stochastic conditional independence are proved. First, the intersection of two conditional independence models is shown to be a conditional independence model. Using this result it is proved that the conditional independence models for natural conditional functions have no finite complete axiomatic characterization (by means of a simple deductive system describing relationships among conditional independence statements). The last part is devoted to the marginal problem for natural conditional functions: it is shown that the (pairwise) consonancy is equivalent to the consistency iff the running intersection property holds.

AMS classification 68T30

natural conditional function
conditional independence
axiomatic characterization
marginal problem
running intersection property

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The paper builds on the following works: