Abstract
The problem of consistently assigning probabilities to logical formulas is an important problem. In this paper a set of logical formulas will be identified for which the problem can be solved. For every directed graph we define a set of logical formulas that it represents. If the underlying (undirected) graph is either perfect or t-perfect a closed form solution to the consistency problem can be given. A remarkable property of the class of formulas identified here is that it turns out to be closed under duality (if a set of formulas is represented by a digraph then the dual set of formulas is also represented by a digraph).
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Andersen, K.A. Characterizing consistency in probabilistic logic for a class of Horn clauses. Mathematical Programming 66, 257–271 (1994). https://doi.org/10.1007/BF01581149
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DOI: https://doi.org/10.1007/BF01581149