Abstract
Some research has been done on probabilistic extension of description logics such as P-CLASSIC and P-\(\mathcal {SHOQ}\) which focus on the statistical information. For example, in those kind of probabilistic DL, we can express such kind of uncertainty that the probability a randomly chosen individual in concept C is also in concept D is 90 percent. This kind of statistical knowledge is certain which means the author of this statement is sure about it. In this paper, we will describe a new kind of probabilistic description logic Pr\(\mathcal{SH}\) which could let user express the uncertain knowledge(i.e. degrees of belief). For example, if the user is not sure about that concept C is subsumed by concept D, he could describe it with Pr\(\mathcal{SH}\) such as the probability that concept C is subsumed by concept D is 90 percent.Furthermore, user could make use of the uncertain knowledge to infer some implicit knowledge by the extension of tableau-algorithm of \(\mathcal {SH}\) which will be also introduced in this paper.
Supported by the National Grand Fundamental Research 973 Program of China Under Grant No. 2002CB312006; the National Natural Science Foundation of China Under Grant Nos. 60473058.
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References
Koller, D., Levy, A.Y., Pfeffer, A.: P-CLASSIC: A tractable probablistic description logic. In: AAAI/IAAI, pp. 390–397 (1997)
Giugno, R., Lukasiewicz, T.: P-\(\mathcal{SHOQ}({\bf D})\): A probabilistic extension of \(\mathcal{SHOQ}({\bf D})\) for probabilistic ontologies in the semantic web. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 86–97. Springer, Heidelberg (2002)
Halpern, J.Y.: An analysis of first-order logics of probability. In: IJCAI, pp. 1375–1381 (1989)
Hacking, I.: Logic of Statistical Inference. Cambridge University Press, Cambridge (1965)
Bacchus, F., Grove, A.J., Halpern, J.Y., Koller, D.: From statistical knowledge bases to degrees of belief. Artif. Intell. 87(1-2), 75–143 (1996)
Noy, N.F.: Semantic integration: A survey of ontology-based approaches. SIGMOD Record 33(4), 65–70 (2004)
Rahm, E., Bernstein, P.A.: A survey of approaches to automatic schema matching. VLDB J. 10(4), 334–350 (2001)
Schmidt-Schauß, M., Smolka, G.: Attributive concept descriptions with complements. Artificial Intelligence 48(1), 1–26 (1991)
Pan, J.Z.: Description Logics: Reasoning Support for the Semantic Web. PhD thesis, School of Computer Science, The University of Manchester, Manchester (2004)
Fagin, R., Halpern, J.Y., Megiddo, N.: A logic for reasoning about probabilities. Inf. Comput. 87(1/2), 78–128 (1990)
Nilsson, N.: Probabilistic logic. AI 28, 71–87 (1986)
Halpern, J.Y.: Reasoning about knowledge: A survey. In: Gabbay, D.M., Hogger, C.J., Robinson, J.A. (eds.) Handbook of Logic in Artificial Intelligence and Logic Programming, Volume 4: Epistemic and Temporal Reasoning, pp. 1–34. Clarendon Press, Oxford (1995)
Fagin, R., Halpern, J.Y.: Uncertainty, belief, and probability. In: IJCAI, pp. 1161–1167 (1989)
Friedman, N., Halpern, J.Y.: Modeling belief in dynamic systems, part I: Foundations. Artif. Intell. 95(2), 257–316 (1997)
Friedman, N., Halpern, J.Y.: Modeling belief in dynamic systems, part II: Revision and update. J. Artif. Intell. Res (JAIR) 10, 117–167 (1999)
Heinsohn, J.: Probabilistic description logics. In: de Mantaras, R.L., Poole, D. (eds.) Proceedings of the 10th Conference on Uncertainty in Artificial Intelligence, July 1994, pp. 311–318. Morgan Kaufmann, San Francisco (1994)
Lukasiewicz, T.: Probabilistic deduction with conditional constraints over basic events. In: KR, pp. 380–393 (1998)
Jaeger, M.: Probabilistic reasoning in terminological logics. In: KR, pp. 305–316 (1994)
Baader, F., Laux, A.: Terminological logics with modal operators. In: IJCAI (1), pp. 808–815 (1995)
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Jia, T., Zhao, W., Wang, L. (2007). Pr\(\mathcal{SH}\): A Belief Description Logic. In: Nguyen, N.T., Grzech, A., Howlett, R.J., Jain, L.C. (eds) Agent and Multi-Agent Systems: Technologies and Applications. KES-AMSTA 2007. Lecture Notes in Computer Science(), vol 4496. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72830-6_4
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