### G-99-11

# On the Relationship between Probabilistic Logic and -CMS

## Pierre Hansen, Brigitte Jaumard, and Anderson D. Parreira

We discuss the relationship between probabilistic logic and -CMS. Given a set of logical sentences and probabilities, 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 -CMS systems, the outcome is defined by the probabilities of the support and the plausibility of a clause (with an assumption on the independence of the events) after a first phase which consists of computing the prime implicants depending only on the variables of the assumptions. We propose to reformulate a -CMS system using the linear programming framework of the probabilistic logic solution tools, and show how to exploit its particularstructure to solve it efficiently, namely how to redefine the subproblem so as to reduce significantly the size of the matrix of the linear program. Due to the independence assumptions and the restrictions on the variable domain of the prime implicants, we observe differences between the probabilities of the two systems. 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).

Published **January 1999**
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14 pages

This cahier was revised in **March 1999**