Abstract
This paper presents a study of the relationship between probabilistic reasoning and deductive reasoning, in propositional format. We propose an algorithm to solve probabilistic satisfiability (PSAT) based on the study of its logical properties. Each iteration of the algorithm generates in polynomial time a classical (non-probabilistic) formula that is submitted to a SAT-oracle. This strategy is a Turing reduction of PSAT into SAT. We demonstrate the correctness and termination of the algorithm.
This work was supported by Fapesp Thematic Project 2008/03995-5 (LOGPROB).
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References
Andersen, K., Pretolani, D.: Easy cases of probabilistic satisfiability. Annals of Mathematics in Artificial Intelligence 33(1), 69–91 (2001)
Boole, G.: An Investigation on the Laws of Thought. Macmillan, London (1854)
Cook, S.A.: The complexity of theorem-proving procedures. In: Third Annual ACM Symposium on Theory of Computing (STOC), pp. 151–158. ACM, New York (1971)
Dixon, H.E., Ginsberg, M.L.: Inference methods for a pseudo-boolean satisfiability solver. In: AAAI/IAAI, pp. 635–640 (2002)
Gent, I.P., Walsh, T.: The SAT phase transition. In: ECAI 1994 – Proceedings of the Eleventh European Conference on Artificial Intelligence, pp. 105–109 (1994)
Georgakopoulos, G., Kavvadias, D., Papadimitriou, C.H.: Probabilistic satisfiability. Journal of Complexity 4(1), 1–11 (1988)
Goldberg, E., Novikov, Y.: Berkmin: A Fast and Robust SAT Solver. In: Design Automation and Test in Europe (DATE 2002), pp. 142–149 (2002)
Gomory, R.: An algorithm for integer solutions to linear programs. In: Recent Advances in Mathematical Programming, pp. 69–302. McGraw-Hill, New York (1963)
Hailperin, T.: Prob. logic. N. D. Journal of Formal Logic 25(3), 198–212 (1984)
Hansen, P., Jaumard, B.: Probabilistic satisability. Technical Report, Les Cahiers du GERAD G-96-31, École Polytechique de Montréal (1996)
Hansen, P., et al.: Probabilistic satisfiability with imprecise probabilities. In: 1st Int. Symposium on Imprecise Probabilities and Their Applications, pp. 165–174 (1999)
Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: Engineering an Efficient SAT Solver. In: Proceedings of the 38th Design Automation Conference (DAC 2001), pp. 530–535 (2001)
Nilsson, N.: Probabilistic logic. Artificial Intelligence 28(1), 71–87 (1986)
Nilsson, N.: Probabilistic logic revisited. Artificial Intelligence 59(1-2), 39–42 (1993)
Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)
Warners, J.P.: A linear-time transformation of linear inequalities into conjunctive normal form. Inf. Process. Lett. 68(2), 63–69 (1998)
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Finger, M., De Bona, G. (2010). A Logic Based Algorithm for Solving Probabilistic Satisfiability. In: Kuri-Morales, A., Simari, G.R. (eds) Advances in Artificial Intelligence – IBERAMIA 2010. IBERAMIA 2010. Lecture Notes in Computer Science(), vol 6433. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16952-6_46
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DOI: https://doi.org/10.1007/978-3-642-16952-6_46
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