Lukasiewicz, T. (1999)
"Probabilistic Deduction with Conditional Constraints over Basic Events",
Volume 10, pages 199-241.
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Abstract: We study the problem of probabilistic deduction with
conditional constraints over basic events. We show that globally
complete probabilistic deduction with conditional constraints over
basic events is NP-hard. We then concentrate on the special case of
probabilistic deduction in conditional constraint trees. We elaborate
very efficient techniques for globally complete probabilistic
deduction. In detail, for conditional constraint trees with point
probabilities, we present a local approach to globally complete
probabilistic deduction, which runs in linear time in the size of the
conditional constraint trees. For conditional constraint trees with
interval probabilities, we show that globally complete probabilistic
deduction can be done in a global approach by solving nonlinear
programs. We show how these nonlinear programs can be transformed into
equivalent linear programs, which are solvable in polynomial time in
the size of the conditional constraint trees.
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