Simplification rules for the coherent probability assessment problem

In this paper we develop a procedure for checking the consistency (coherence) of a partial probability assessment. The general problem (called CPA) is NP-complete, hence, to have a reasonable application some heuristic is needed. Our proposal differs from others because it is based on a skilful use of the logical relations present among the events. In other approaches the consistency problem is reduced directly to the satisfiability of a system of linear constraints. Here, thanks to the characterization of particular configurations and to the elimination of variables, an instance of the problem is reduced to smaller instances. To obtain such results, we introduce a procedure based on rules resembling those given by Davis-Putnam for the satisfiability of Boolean formulas. At the end a particularized description of an actual implementation is given.