On the Relations between Probabilistic Logic and p-CMS

Abstract

We discuss the relationship between probabilistic logic and 1r-CMS. Given a set of logical sentences and their probabilities of being true, the outcome of a probabilistic logic system consists of lower and upper bounds on the probability of an additional sentence to be true . These bounds are computed using a linear programming formulation. In 1r-CMS systems, the outcome is defined by the probabilities of the support and the plausibility (with the assumptions being independent) after a first phase which consists of computing the prime implicants depending only on the variables of the assumptions. We propose to reformulate a 7rCMS system without independence conditions on the assumptions, using the linear programming framework of probabilistic logic, and show how to exploit its particular structure to solve it efficiently. When an independence condition is imposed on the assumptions the two systems give different results. Comparisons are made on small problems using the assumption-based evidential language program (ABEL) of [Anrig et al., 1998] and the PSAT program of [Jaumard et al., 1991].