Determining lower and upper bounds on probabilities of atomic propositions in sets of logical formulas represented by digraphs |
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Authors: | K A Andersen J N Hooker |
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Institution: | (1) Matematisk Institut, Aarhus Universitet, DK-8000 Århus C, Denmark;(2) Graduate School of Industrial Administration, Carnegie Mellon University, 15213 Pittsburgh, PA, USA |
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Abstract: | 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.The second author is partially supported by ONR grant N00014-92-J-1028 and AFOSR grant 91-0287. |
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