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.
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The second author is partially supported by ONR grant N00014-92-J-1028 and AFOSR grant 91-0287.
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Andersen, K.A., Hooker, J.N. Determining lower and upper bounds on probabilities of atomic propositions in sets of logical formulas represented by digraphs. Ann Oper Res 65, 1–20 (1996). https://doi.org/10.1007/BF02187324
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DOI: https://doi.org/10.1007/BF02187324