Artificial Intelligence
A theory of diagnosis from first principles
Artificial Intelligence
A quantitative approach to logical inference
Decision Support Systems
Column Generation Methods for Probabilistic Logic
Proceedings of the 1st Integer Programming and Combinatorial Optimization Conference
Pellet: A practical OWL-DL reasoner
Web Semantics: Science, Services and Agents on the World Wide Web
Merging the local and global approaches to probabilistic satisfiability
International Journal of Approximate Reasoning
Expressive probabilistic description logics
Artificial Intelligence
Models and algorithms for probabilistic and Bayesian logic
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 2
The Consistency of the Medical Expert System CADIAG-2: A Probabilistic Approach
Journal of Information Technology Research
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Determining satisfiability of sets of formula formulated in a Nilsson style probabilistic logic (PSAT) by reduction to a system of linear (in)equations has been extensively studied, esp. in the propositional setting. The basic technique for coping with the potentially exponentially large (in terms of the formulae) linear system is column generation, which has been successful (in various forms) in solving problems of around 1000 formulae. Common to existing techniques is that the column generation model explicitly encodes all classical, i.e., non-probabilistic, knowledge. In this paper we introduce a straightforward but new hybrid method for PSAT that makes use of a classical solver in the column generation process. The benefits of this technique are twofold: first, we can, in practice, accommodate inputs with significantly larger classical parts, and thus which are overall larger, and second, we can accommodate inputs with supra-propositional classical parts, such as propositionally complete description logics. We validate our approach with an extensive series of experiments which show that our technique is competitive with traditional non-hybrid approaches in spite of scaling the expressivity of the classical part to the description logic SROIQ.