Abstract

We propose a symmetric definition of conditional independence between sets of variables in possibility theory, and relate it to the notion of lack of interaction. Possibilistic independence expresses irrelevance of some pieces of information for belief updating, and it is shown that, for three large classes of operators (Łukasiewicz-like T-norms, productlike T-norms, minimum operator), this relation is a graphoid. Possibilistic lack of interaction is a weaker notion than independence: it only requires the joint possibility distribution to be factorized. It is shown here that this relation is, in the three special cases cited above, a semigraphoid, but generally lacks the intersection property.

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