Abstract
Knowledge is an important component in many intelligent systems. Since items of knowledge in a knowledge base can be conflicting, especially if there are multiple sources contributing to the knowledge in this base, significant research efforts have been made on developing inconsistency measures for knowledge bases and on developing merging approaches. Most of these efforts start with flat knowledge bases. However, in many real-world applications, items of knowledge are not perceived with equal importance, rather, weights (which can be used to indicate the importance or priority) are associated with items of knowledge. Therefore, measuring the inconsistency of a knowledge base with weighted formulae as well as their merging is an important but difficult task. In this paper, we derive a numerical characteristic function from each knowledge base with weighted formulae, based on the Dempster-Shafer theory of evidence. Using these functions, we are able to measure the inconsistency of the knowledge base in a convenient and rational way, and are able to merge multiple knowledge bases with weighted formulae, even if knowledge in these bases may be inconsistent. Furthermore, by examining whether multiple knowledge bases are dependent or independent, they can be combined in different ways using their characteristic functions, which cannot be handled (or at least have never been considered) in classic knowledge based merging approaches in the literature.
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References
Bacchus, F., Grove, A., Halpern, J., Koller, D.: From statistical knowledge bases to degrees of belief. Artificial Intelligence 87(1-2), 75–143 (1996)
Benferhat, S., Dubois, D., Prade, H.: Representing default rules in possibilistic logic. In: Procs. of KR, pp. 673–684 (1992)
Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. The Annals of Statistics 28, 325–339 (1967)
Dempster, A.P.: A generalization of bayesian inference. J. Roy. Statist. Soc. 30, Series B, 205–247 (1968)
Denœux, T.: Conjunctive and disjunctive combination of belief functions induced by nondistinct bodies of evidence. Artifical Intelligence 172(2-3), 234–264 (2008)
Dubois, D., Prade, H.: Representation and combination of uncertainty with belief functions and possibility measures. Computational Intelligence 4, 244–264 (1988)
Hunter, A., Konieczny, S.: Shapley inconsistency values. In: Procs. of KR 2006, pp. 249–259 (2006)
Hunter, A., Konieczny, S.: Measuring inconsistency through minimal inconsistent sets. In: Procs. of KR, pp. 358–366 (2008)
Konieczny, S., Pino-Pérez, R.: On the logic of merging. In: Cohn, A.G., Schubert, L., Shapiro, S.C. (eds.) Principles of Knowledge Representation and Reasoning, KR 1998, pp. 488–498. Morgan Kaufmann, San Francisco (1998)
Lin, J.: Integration of weighted knowledge bases. Artif. Intel. 83(2), 363–378 (1996)
Liu, W.: Analyzing the degree of conflict among belief functions. Artificial Intelligence 170, 909–924 (2006)
Ma, J., Liu, W., Hunter, A.: Incomplete Statistical Information Fusion and Its Application to Clinical Trials Data. In: Prade, H., Subrahmanian, V.S. (eds.) SUM 2007. LNCS (LNAI), vol. 4772, pp. 89–103. Springer, Heidelberg (2007)
Ma, J., Liu, W., Hunter, A.: The Non-archimedean Polynomials and Merging of Stratified Knowledge Bases. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS, vol. 5590, pp. 408–420. Springer, Heidelberg (2009)
Ma, J., Liu, W., Hunter, A.: Inducing probability distributions from knowledge bases with (in)dependence relations. In: Procs. of AAAI, pp. 339–344 (2010)
Ma, J., Liu, W., Hunter, A.: Inducing probability distributions from knowledge bases with (in)dependence relations. In: Proceedings of the 24th American National Conference on Artificial Intelligence, AAAI 2010 (2010)
Ma, J., Liu, W.: A framework for managing uncertain inputs: an axiomization of rewarding. International Journal of Approximate Reasoning 52(7), 917–934 (2011)
Ma, J., Liu, W., Miller, P.: Event Modelling and Reasoning with Uncertain Information for Distributed Sensor Networks. In: Deshpande, A., Hunter, A. (eds.) SUM 2010. LNCS, vol. 6379, pp. 236–249. Springer, Heidelberg (2010)
Ma, J., Liu, W., Miller, P., Yan, W.: Event composition with imperfect information for bus surveillance. In: Procs. of AVSS, pp. 382–387. IEEE Press (2009)
Miller, P., Liu, W., Fowler, F., Zhou, H., Shen, J., Ma, J., Zhang, J., Yan, W., McLaughlin, K., Sezer, S.: Intelligent sensor information system for public transport: To safely go... In: Procs. of AVSS, pp. 533–538 (2010)
Mu, K., Jin, Z., Lu, R., Liu, W.: Measuring Inconsistency in Requirements Specifications. In: Godo, L. (ed.) ECSQARU 2005. LNCS (LNAI), vol. 3571, pp. 440–451. Springer, Heidelberg (2005)
Mu, K., Liu, W., Jin, Z.: A blame-based approach to generating proposals for handling inconsistency in software requirements. International Journal of Knowledge and Systems Science 3(1), 1–16 (2012)
Rossini, P.: Using expert systems and artificial intelligence for real estate forecasting. In: Procs. of Sixth Annual Pacific-Rim Real Estate Society Conference, Sydney, Australia, January 24-27, pp. 1–10 (2000)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press (1976)
Smets, P.: Belief functions. In: Smets, P., Mamdani, A., Dubois, D., Prade, H. (eds.) Non-Standard Logics for Automated Reasoning, pp. 253–286 (1988)
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Ma, J., Liu, W., Miller, P. (2012). A Characteristic Function Approach to Inconsistency Measures for Knowledge Bases. In: Hüllermeier, E., Link, S., Fober, T., Seeger, B. (eds) Scalable Uncertainty Management. SUM 2012. Lecture Notes in Computer Science(), vol 7520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33362-0_36
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DOI: https://doi.org/10.1007/978-3-642-33362-0_36
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