Abstract
Uncertainty reasoning and inconsistency handling are two important problems that often occur in the applications of the Semantic Web. Possibilistic description logics provide a flexible framework for representing and reasoning with ontologies where uncertain and/or inconsistent information is available. Although possibilistic logic has become a popular logical framework for uncertainty reasoning and inconsistency handling, its role in the Semantic Web is underestimated. One of the challenging problems is to provide a practical algorithm for reasoning in possibilistic description logics. In this paper, we propose a tableau algorithm for possibilistic description logic \(\mathcal{ALC}\). We show how inference services in possibilistic \(\mathcal{ALC}\) can be reduced to the problem of computing the inconsistency degree of the knowledge base. We then give tableau expansion rules for computing the inconsistency degree of a possibilistic \(\mathcal{ALC}\) knowledge. We show that our algorithm is sound and complete. The computational complexity of our algorithm is analyzed. Since our tableau algorithm is an extension of a tableau algorithm for \(\mathcal{ALC}\), we can reuse many optimization techniques for tableau algorithms of \(\mathcal{ALC}\) to improve the performance of our algorithm so that it can be applied in practice.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. (eds.): The description logic handbook: theory, implementation, and applications. Cambridge University Press, New York (2003)
Baader, F., Hollunder, B., Nebel, B., Profitlich, H.-J., Franconi, E.: An empirical analysis of optimization techniques for terminological representation systems, or making kris get a move on. In: Proc. of KR 1992, pp. 270–281 (1992)
Baader, F., Horrocks, I., Sattler, U.: Description Logics. In: van Harmelen, F., Lifschitz, V., Porter, B. (eds.) Handbook of Knowledge Representation. Elsevier, Amsterdam (to appear, 2007)
Baaderand, F., Sattler, U.: An overview of tableau algorithms for description logics. Studia Logica 69(1), 5–40 (2001)
Couchariere, O., Lesot, M.-J., Bouchon-Meunier, B.: Consistency checking for extended description logics. In: Description Logics (2008)
Dubois, D., Lang, J., Prade, H.: Automated reasoning using possibilistic logic: Semantics, belief revision, and variable certainty weights. IEEE Trans. Knowl. Data Eng. 6(1), 64–71 (1994)
Dubois, D., Lang, J., Prade, H.: Possibilistic logic. In: Handbook of logic in Aritificial Intelligence and Logic Programming, 3rd edn., pp. 439–513. Oxford University Press, Oxford (1994)
Dubois, D., Mengin, J., Prade, H.: Possibilistic uncertainty and fuzzy features in description logic: A preliminary discussion. In: Capturing Intelligence: Fuzzy Logic and the Semantic WEb, pp. 101–113. Elsevier, Amsterdam (2006)
Giugno, R., Lukasiewicz, T.: P-\(\mathcal{SHOQ}({d})\): A probabilistic extension of \(\mathcal{SHOQ}({d})\) for probabilistic ontologies in the semantic web. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS, vol. 2424, pp. 86–97. Springer, Heidelberg (2002)
Heinsohn, J.: Probabilistic description logics. In: Proc. of UAI 1994, pp. 311–318 (1994)
Hollunder, B.: An alternative proof method for possibilistic logic and its application to terminological logics. In: Proc. of UAI 1994, pp. 327–335 (1994)
Jaeger, M.: Probabilistic reasoning in terminological logics. In: Proc. of KR 1994, pp. 305–316 (1994)
Koller, D., Levy, A.Y., Pfeffer, A.: P-classic: A tractable probablistic description logic. In: Proc. of AAAI/IAAI 1997, pp. 390–397 (1997)
Lang, J.: Possibilistic logic: complexity and algorithms. In: Handbook of Defeasible Reasoning and Uncertainty Management Systems, pp. 179–220. Kluwer, Dordrecht (1998)
Lukasiewicz, T.: Probabilistic default reasoning with conditional constraints. Ann. Math. Artif. Intell. 34(1-3), 35–88 (2002)
Lukasiewicz, T.: Expressive probabilistic description logics. Artif. Intell. 172(6-7), 852–883 (2008)
Lutz, C.: Complexity of terminological reasoning revisited. In: LPAR 1999, pp. 181–200 (1999)
Qi, G., Pan, J.Z., Ji, Q.: Extending description logics with uncertainty reasoning in possibilistic logic. In: Mellouli, K. (ed.) ECSQARU 2007. LNCS, vol. 4724, pp. 828–839. Springer, Heidelberg (2007)
Stoilos, G., Stamou, G., Pan, J.Z., Tzouvaras, V., Horrocks, I.: Reasoning with very expressive fuzzy description logics. J. Artif. Intell. Res. 30, 273–320 (2007)
Straccia, U.: Reasoning within fuzzy description logics. J. Artif. Intell. Res. 14, 137–166 (2001)
Udrea, O., Deng, Y., Hung, E., Subrahmanian, V.S.: Probabilistic ontologies and relational databases. In: Proc. of CoopIS/DOA/ODBASE 2005, pp. 1–17 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Qi, G., Pan, J.Z. (2008). A Tableau Algorithm for Possibilistic Description Logic \(\mathcal{ALC}\) . In: Domingue, J., Anutariya, C. (eds) The Semantic Web. ASWC 2008. Lecture Notes in Computer Science, vol 5367. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89704-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-89704-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89703-3
Online ISBN: 978-3-540-89704-0
eBook Packages: Computer ScienceComputer Science (R0)