Belief Maintenance with Probabilistic Logic

Belief maintenance systems are natural extensions of truth maintenance systems that use probabilities rather than boolean truth-values. This paper introduces a general method for belief maintenance, based on (the propositional fragment of) probabilistic logic, that extends the Boolean Constraint Propagation method used by the logic-based truth maintenance systems. From the concept of probabilistic entailment, we derive a set of constraints on the (probabilistic) truth-values of propositions and we prove their soundness. These constraints are complete with respect to a well-defined set of clauses, and their partial incompleteness is compensated by a gain in computational efficiency.