Abstract
Most techniques for probabilistic reasoning focus on reasoning about conditional probability constraints. However, human experts are accustomed to representing uncertain knowledge in the form of expectation rather than probability distribution directly in many cases. It is necessary to provide a logic for encoding hybrid probabilistic knowledge bases that contain expectation knowledge as well as the purely probabilistic knowledge in the form of conditional probability. This paper constructs a nonmonotonic logic for reasoning about hybrid probabilistic knowledge bases. We extend the propositional logic for reasoning about expectation to encoding hybrid probabilistic knowledge by introducing the conditional expectation constraint formula. Then we provide an approach to nonmonotonic reasoning about hybrid probabilistic knowledge bases. Finally,we compare this logic with related works.
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References
Lukasiewicz, T.: Nonmonotonic probabilistic logics under variable-strength inheritance with overriding:algorithms and implementation in nmproblog. In: 4th International Symposium on Imprecise Probabilities and Their Applications, pp. 230–239 (2005)
Fagin, R., Halpern, J., Megiddo, N.: A logic for reasoning about probabilities. Information and Computation 87, 78–128 (1990)
Dubois, D., Prade, H.: Inference with imprecise numerical quantifiers (1990)
Lukasiewicz, T.: Weak nonmonotonic probabilistic logics. In: Proceedings KR 2004, pp. 22–33 (2004)
Lukasiewicz, T.: Probabilistic default reasoning with conditional constraints. Annals of Mathematics and Artificial Intelligence 34, 35–88 (2002)
Halpern, J., Pucella, R.: Reasoning about expectation. In: Proceedings of the Eighteenth Conference on Uncertainty in AI, pp. 207–215 (2002)
Kraus, S., Lehmann, D., Magidor, M.: Non-monotonic reasoning, preferential models and cumulative logics. Artif. Intell. 14, 167–207 (1990)
Benferhat, S., Saffiotti, A., Smets, P.: Belief functions and default reasoning. Artif. Intell. 122, 1–69 (2000)
Bacchus, F., Grove, A., Halpern, J., Koller, D.: From statical knowledge bases to degrees of beliefs. Artif.Intell. 87, 75–143 (1996)
Pearl, J.: System z: A natural ordering of default with tractable applications in default reasoning. In: Proceedings of TARK 1990, pp. 121–135 (1990)
Lehmann, D.: Another perspective on default reasoning. Ann. Math. Artif. Intell. 15, 61–82 (1995)
Geffner, H.: Causal and conditional theories. MIT Press, Combridge (1992)
Geffner, H., Pearl, J.: Conditional entailment: Bridging two approach to default reasoning. Artif.Intell. 53, 209–244 (1992)
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© 2006 Springer-Verlag Berlin Heidelberg
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Mu, K., Lin, Z., Jin, Z., Lu, R. (2006). Reasoning About Hybrid Probabilistic Knowledge Bases. In: Yang, Q., Webb, G. (eds) PRICAI 2006: Trends in Artificial Intelligence. PRICAI 2006. Lecture Notes in Computer Science(), vol 4099. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36668-3_16
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DOI: https://doi.org/10.1007/978-3-540-36668-3_16
Publisher Name: Springer, Berlin, Heidelberg
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