Implementing an Efficient SAT Solver for a Probabilistic Description Logic

This paper presents an optimized algorithm for solving the satisfiability problem (PSAT) in the probabilistic description logic P-SROIQ. In P-SROIQ and related Nilsson-style probabilistic logics the PSAT problem is typically solved by reduction to linear program-ming. This straightforward approach does not scale well because the number of variables in linear programs grows exponentially with the number of probabilistic statements. In this paper we demonstrate an algorithm to cope with this problem which is based on column generation. Although column generation approaches to PSAT have been known for the last two decades, this is, to the best of our knowledge, the first algorithm which also works for a non-propositional probabilistic logic. We report results of an empirical investigation which show that the algorithm can handle probabilistic knowledge bases of about 1000 probabilistic statements in addition to even larger number of classical SROIQ axioms.