Generalized probabilistic satisfiability through integer programming

Andersen KA, Pretolani D (2001) Easy cases of probabilistic satisfiability. Ann Math Artif Intell 33(1): 69–91.

Baioletti M, Capotorti A, Tiberi P, Tulipani S (2004) An empirical complexity for a 2CPA solver. 10th International Conference IPMU: 1857–1864.

Boole G (1958) An Investigation on the Laws of Thought, Dover, New York.

Bruno G, Gilio A (1980) Applicazione del metodo del simplesso al teorema fondamentale per le probabilità nella concezione soggettivistica. Statistica 40: 337–344.

Chandru V, Hooker J (1999) Optimization Methods for Logical Inference, John Wiley & Sons Inc. ISBN: 978-0-471-57035-6.

Cozman FG, di Ianni LF (2013) Probabilistic satisfiability and coherence checking through integer programming In: Symbolic and Quantitative Approaches to Reasoning with Uncertainty, 145–156, The Netherlands.

De Bona G, Cozman FG, Finger M (2014) Towards classifying propositional probabilistic logics. J Appl Logic 12(3): 349–362.

Eckhoff J (1993) Helly, Radon, and Carathéodory type theorems. In: Grüber P Wills J (eds)Handbook of convex geometry, 389–448, North-Holland, Amsterdam, 1993.

Fagin R, Halpern JY, Megiddo N (1990) A logic for reasoning about probabilities. Inform Comput 87: 78–128.

Fagin R, Halpern JY (1994) Reasoning about knowledge and probability. J ACM 41(2): 340–367.

Finger M, De Bona G (2011) Probabilistic satisfiability: Logic-based algorithms and phase transition In: IJCAI, 528–533. doi:10.5591/978-1-57735-516-8/IJCAI11-096.

Gent IP, Walsh T (1994) The SAT phase transition In: 11th European Conference on Artificial Intelligence, 105–109.

Georgakopoulos G, Kavvadias D, Papadimitriou CH (1988) Probabilistic satisfiability. J Complexity 4: 1–11.

Hailperin T (1965) Best possible inequalities for the probability of a logical function of events. 72: 343–359.

Hailperin T (1976) Boole’s Logic and Probability: a Critical Exposition from the Standpoint of Contemporary Algebra, Logic, and Probability Theory, North-Holland, Amsterdam.

Halpern JY (2003) Reasoning about Uncertainty. MIT Press, Cambridge, Massachusetts.

Hansen P, Jaumard B (1996) Probabilistic Satisfiability. Technical Report G-96-31, Les Cahiers du GERAD, École Polytechique de Montréal.

Hansen P, Perron S (2008) Merging the local and global approaches to probabilistic satisfiability. Int J Approximate Reasoning 47(2): 125–140.

Jaumard B, Hansen P, de Aragão MP (1991) Column generation methods for probabilistic logic. ORSA J Comput 3(2): 135–148.

Lukasiewicz T (2008) Expressive probabilistic description logics. Artif Intell 172(6–7): 852–883.

Ng R, Subrahmanian VS (1992) Probabilistic logic programming. Inform Comput 101(2): 150–201.

Nilsson NJ (1986) Probabilistic logic. Artif Intell 28: 71–87.

Uchii S (1973) Higher order probabilities and coherence. Philos Sci 40(3): 373–381.

Williams HP (2009) Logic and integer programming. Springer. ISBN 978-0-387-92280-5.