Determining Lower and Upper Bounds on Probabilities of Atomic Propositions in Sets of Logical Formulas Represented by Digraphs
journal contributionposted on 01.01.1996 by K. A. Andersen, John N. Hooker
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In this paper we consider the problem of determining lower and upper bounds on probabilities of atomic propositions in sets of logical formulas represented by digraphs. We establish a sharp upper bound, as well as a lower bound that is not in general sharp. We show further that under a certain condition the lower bound is sharp. In that case, we obtain a closed form solution for the possible probabilities of the atomic propositions.