Abstract
We present a reasoning procedure for ontologies with uncertainty described in Description Logic (DL) which include General TBoxes, i.e., include cycles and General Concept Inclusions (GCIs). For this, we consider the description language \({{\cal{ALC}}_U}\), in which uncertainty parameters are associated with ABoxes and TBoxes, and which allows General TBoxes. Using this language as a basis, we then present a tableau algorithm which encodes the semantics of the input knowledge base as a set of assertions and linear and/or nonlinear arithmetic constraints on certainty variables. By tuning the uncertainty parameters in the knowledge base, different notions of uncertainty can be modeled and reasoned with, within the same framework. Our reasoning procedure is deterministic, and hence avoids possible empirical intractability in standard DL with General TBoxes. We further illustrate the need for blocking when reasoning with General TBoxes in the context of \({{\cal{ALC}}_U}\).
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, Cambridge (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: Nebel, B., Swartout, W., Rich, C. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the 3rd International Conference, San Mateo, pp. 270–281. Morgan Kaufmann, San Francisco (1992)
Baader, F., Horrocks, I., Sattler, U.: Description Logics. In: van Harmelen, F., Lifschitz, V., Porter, B. (eds.) Handbook of Knowledge Representation. Elsevier, Amsterdam (2007)
Bobillo, F., Delgado, M., Gomez-Romero, J.: A crisp representation for fuzzy \({\cal{SHOIN}}\) with fuzzy nominals and general concept inclusions. In: Proceedings of the 2nd Workshop on Uncertainty Reasoning for the Semantic Web (URSW), Athens, Georgia, USA (November 2006)
Bobillo, F., Straccia, U.: A fuzzy description logic with product t-norm. In: Proceedings of the IEEE International Conference on Fuzzy Systems (Fuzz IEEE 2007), pp. 652–657. IEEE Computer Society, Los Alamitos (2007)
Dürig, M., Studer, T.: Probabilistic ABox reasoning: Preliminary results. In: Proceedings of the International Workshop on Description Logics (DL 2005), pp. 104–111 (2005)
Giugno, R., Lukasiewicz, T.: P-\(\cal{SHOQ}\)(D): A probabilistic extension of \(\cal{SHOQ}\)(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)
Haarslev, V., Pai, H.I., Shiri, N.: A generic framework for description logics with uncertainty. In: Proceedings of the 2005 Workshop on Uncertainty Reasoning for the Semantic Web (URSW) at the 4th International Semantic Web Conference, Galway, Ireland, pp. 77–86 (November 2005)
Haarslev, V., Pai, H.I., Shiri, N.: Completion rules for uncertainty reasoning with the description logic \({\cal{ALC}}\). In: Proceedings of the Canadian Semantic Web Working Symposium - Semantic Web and Beyond: Computing for Human Experience, Quebec City, Canada, vol. 4, pp. 205–225. Springer, Heidelberg (2006)
Haarslev, V., Pai, H.I., Shiri, N.: Uncertainty reasoning in description logics: A generic approach. In: Proceedings of the 19th International FLAIRS Conference, Melbourne Beach, Florida, pp. 818–823. AAAI Press, Menlo Park (2006)
Haarslev, V., Pai, H.I., Shiri, N.: Optimizing tableau reasoning in \({\cal{ALC}}\) extended with uncertainty. In: Proceedings of the International Workshop on Description Logics (DL 2007), Brixen-Bressanone, Italy, pp. 307–314 (June 2007)
Haarslev, V., Pai, H.I., Shiri, N.: Semantic web uncertainty management. In: Encyclopedia of Information Science and Technology, 2nd edn., Information Science Reference (2008)
Jaeger, M.: Probabilistic reasoning in terminological logics. In: Proceedings of the 4th International Conference on Principles of Knowledge Representation and Reasoning (KR 1994), pp. 305–316 (1994)
Koller, D., Levy, A.Y., Pfeffer, A.: P-CLASSIC: A tractable probablistic description logic. In: Proceedings of the 14th National Conference on Artificial Intelligence, Providence, Rhode Island, pp. 390–397. AAAI Press, Menlo Park (1997)
Lakshmanan, L.V.S., Shiri, N.: Logic programming and deductive databases with uncertainty: A survey. In: Enclyclopedia of Computer Science and Technology, vol. 45, pp. 153–176. Marcel Dekker, Inc., New York (2001)
Lakshmanan, L.V.S., Shiri, N.: A parametric approach to deductive databases with uncertainty. IEEE Transactions on Knowledge and Data Engineering 13(4), 554–570 (2001)
Pai, H.I. Uncertainty Management for Description Logic-Based Ontologies. PhD thesis, Concordia University (2008)
Schild, K.: A correspondence theory for terminological logics: preliminary report. In: Proceedings of IJCAI 1991, 12th International Joint Conference on Artificial Intelligence, Sidney, AU, pp. 466–471 (1991)
Stoilos, G., Stamou, G., Pan, J.Z., Tzouvaras, V., Horrocks, I.: Reasoning with very expressive fuzzy description logics. Journal of Artificial Intelligence Research 30, 273–320 (2007)
Stoilos, G., Straccia, U., Stamou, G., Pan, J.Z.: General concept inclusions in fuzzy description logics. In: Proceedings of the 17th European Conference on Artificial Intelligence (ECAI 2006) (2006)
Straccia, U.: Reasoning within fuzzy description logics. Journal of Artificial Intelligence Research 14, 137–166 (2001)
Straccia, U.: Uncertainty in description logics: a lattice-based approach. In: Proceedings of the 10th International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, pp. 251–258 (2004)
Straccia, U. Fuzzy description logic with concrete domains. Technical Report 2005-TR-03, Istituto di Elaborazione dell’Informazione (January 2005)
Straccia, U., Bobillo, F.: Mixed integer programming, general concept inclusions and fuzzy description logics. In: Proceedings of the 5th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT 2007), Ostrava, Czech Republic, vol. 2, pp. 213–220. University of Ostrava (2007)
Tresp, C., Molitor, R.: A description logic for vague knowledge. In: Proceedings of ECAI 1998, Brighton, UK, pp. 361–365. John Wiley and Sons, Chichester (1998)
W3C. OWL web ontology language overview (2004), http://www.w3.org/TR/owl-features/
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
Haarslev, V., Pai, HI., Shiri, N. (2008). Uncertainty Reasoning for Ontologies with General TBoxes in Description Logic. In: da Costa, P.C.G., et al. Uncertainty Reasoning for the Semantic Web I. URSW URSW URSW 2006 2007 2005. Lecture Notes in Computer Science(), vol 5327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89765-1_22
Download citation
DOI: https://doi.org/10.1007/978-3-540-89765-1_22
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89764-4
Online ISBN: 978-3-540-89765-1
eBook Packages: Computer ScienceComputer Science (R0)