Groupe d’études et de recherche en analyse des décisions

# Analytical Solution for Probabilistic Logic with Conditional Probabilities

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

Given a set of logical sentences and probabilities that these sentences are true, the probabilistic logic problem consists in determining whether these probabilities are consistent. When so, the probabilistic entailment problem is to determine the range of values of the probability associated with an additional logical sentence such that the resulting system of sentences and probabilities remains consistent. These problems are well-solved, both analytically and numerically. In this note, we propose an analytical solution method for their extension where conditional probabilities are given instead of or in addtion to probabilities. This method is illustrated by automated deduction, and improvement in one case, of inference rules with conditional probabilities gathered by Frisch and Haddawy (1994).

, 29 pages