CHARACTERIZING CONSISTENCY IN PROBABILISTIC LOGIC FOR A CLASS OF HORNCLAUSES

The problem of consistently assigning probabilities to logical formula s is an important problem. In this paper a set of logical formulas wil l be identified for which the problem can be solved. For every directe d 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 p roperty 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 d igraph then the dual set of formulas is also represented by a digraph) .