Towards Precision of Probabilistic Bounds Propagation

The DUCK-calculus presented here is a re­ cent approach to cope with probabilistic un­ certainty in a sound and efficient way. Un­ certain rules with bounds for probabilities and explicit conditional independences can be maintained incrementally. The basic in­ ference mechanism relies on local bounds propagation, implementable by deductive databases with a bottom-up fixpoint evalu­ ation. In situations, where no precise bounds are deducible, it can be combined with sim­ ple operations research techniques on a lo­ cal scope. In particular, we provide new pre­ cise analytical bounds for probabilistic entail­ ment.