Abstract
We investigate the modeling of uncertain concepts via rough description logics (RDLs), which are an extension of traditional description logics (DLs) by a mechanism to handle approximate concept definitions via lower and upper approximations of concepts based on a rough-set semantics. This allows to apply RDLs to modeling uncertain knowledge. Since these approximations are ultimately grounded on an indiscernibility relation, we explore possible logical and numerical ways for defining such relations based on the considered knowledge. In particular, we introduce the notion of context, allowing for the definition of specific equivalence relations, which are directly used for lower and upper approximations of concepts. The notion of context also allows for defining similarity measures, which are used for introducing a notion of tolerance in the indiscernibility. Finally, we describe several learning problems in our RDL framework.
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., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic Handbook. Cambridge University Press (2003)
d’Amato, C., Fanizzi, N., Esposito, F.: Query Answering and Ontology Population: An Inductive Approach. In: Bechhofer, S., Hauswirth, M., Hoffmann, J., Koubarakis, M. (eds.) ESWC 2008. LNCS, vol. 5021, pp. 288–302. Springer, Heidelberg (2008)
De Comité, F., Denis, F., Gilleron, R., Letouzey, F.: Positive and Unlabeled Examples Help Learning. In: Watanabe, O., Yokomori, T. (eds.) ALT 1999. LNCS (LNAI), vol. 1720, pp. 219–230. Springer, Heidelberg (1999)
Doherty, P., Grabowski, M., Łukaszewicz, W., Szalas, A.: Towards a framework for approximate ontologies. Fundamenta Informaticae 57(2-4), 147–165 (2003)
Donini, F., Lenzerini, M., Nardi, D., Nutt, W.: An epistemic operator for description logics. Artificial Intelligence 100(1/2), 225–274 (1998)
Fanizzi, N., d’Amato, C., Esposito, F.: Randomized metric induction and evolutionary conceptual clustering for semantic knowledge bases. In: Proceedings of the 16th Conference on Information and Knowledge Management, CIKM 2007, pp. 51–60. ACM Press (2007)
Fanizzi, N., d’Amato, C., Esposito, F.: DL-FOIL Concept Learning in Description Logics. In: Železný, F., Lavrač, N. (eds.) ILP 2008. LNCS (LNAI), vol. 5194, pp. 107–121. Springer, Heidelberg (2008)
Fanizzi, N., d’Amato, C., Esposito, F.: Conceptual Clustering and Its Application to Concept Drift and Novelty Detection. In: Bechhofer, S., Hauswirth, M., Hoffmann, J., Koubarakis, M. (eds.) ESWC 2008. LNCS, vol. 5021, pp. 318–332. Springer, Heidelberg (2008)
Fanizzi, N., d’Amato, C., Esposito, F.: Statistical Learning for Inductive Query Answering on OWL Ontologies. In: Sheth, A.P., Staab, S., Dean, M., Paolucci, M., Maynard, D., Finin, T., Thirunarayan, K. (eds.) ISWC 2008. LNCS, vol. 5318, pp. 195–212. Springer, Heidelberg (2008)
Fanizzi, N., d’Amato, C., Esposito, F., Lukasiewicz, T.: Representing uncertain concepts in rough description logics via contextual indiscernibility relations. In: Proceedings of the 4th International Workshop on Uncertainty Reasoning for the Semantic Web, URSW 2008. CEUR Workshop Proceedings, vol. 423. CEUR-WS.org (2008)
Fanizzi, N., d’Amato, C., Esposito, F.: Induction of Concepts in Web Ontologies through Terminological Decision Trees. In: Balcázar, J.L., Bonchi, F., Gionis, A., Sebag, M. (eds.) ECML PKDD 2010, Part I. LNCS, vol. 6321, pp. 442–457. Springer, Heidelberg (2010)
Goldstone, R., Medin, D., Halberstadt, J.: Similarity in context. Memory and Cognition 25(3), 237–255 (1997)
Hirano, S., Tsumoto, S.: An indiscernibility-based clustering method. In: Proceedings of the 2005 IEEE International Conference on Granular Computing, pp. 468–473. IEEE Computer Society (2005)
Iannone, L., Palmisano, I., Fanizzi, N.: An algorithm based on counterfactuals for concept learning in the Semantic Web. Applied Intelligence 26(2), 139–159 (2007)
Lehmann, J., Hitzler, P.: A Refinement Operator Based Learning Algorithm for the \({\cal ALC}\) Description Logic. In: Blockeel, H., Ramon, J., Shavlik, J., Tadepalli, P. (eds.) ILP 2007. LNCS (LNAI), vol. 4894, pp. 147–160. Springer, Heidelberg (2008)
Lehmann, J.: DL-Learner: Learning concepts in description logics. Journal of Machine Learning Research 10, 2639–2642 (2009)
Lukasiewicz, T., Straccia, U.: Managing uncertainty and vagueness in description logics for the Semantic Web. Journal of Web Semantics 6(4), 291–308 (2008)
Jiang, Y., Wang, J., Tang, S., Xiao, B.: Reasoning with rough description logics: An approximate concepts approach. Information Sciences 179(5), 600–612 (2009)
Keet, C.M.: On the feasibility of description logic knowledge bases with rough concepts and vague instances. In: Proceedings of the 23rd International Workshop on Description Logics, DL 2010. CEUR Workshop Proceedings, vol. 573. CEUR-WS.org (2010)
Keet, C.M.: Ontology Engineering with Rough Concepts and Instances. In: Cimiano, P., Pinto, H.S. (eds.) EKAW 2010. LNCS, vol. 6317, pp. 503–513. Springer, Heidelberg (2010)
Mitchell, T.: Machine Learning. McGraw-Hill (1997)
Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers (1991)
Schlobach, S., Klein, M.C.A., Peelen, L.: Description logics with approximate definitions — precise modeling of vague concepts. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence, IJCAI 2007, pp. 557–562 (2007)
Zezula, P., Amato, G., Dohnal, V., Batko, M.: Similarity Search — The Metric Space Approach. Advances in Database Systems. Springer (2007)
Zhang, B., Zuo, W.: Learning from positive and unlabeled examples: A survey. In: Proceeding of the International Symposium on Information Processing, ISP 2008, pp. 650–654 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
d’Amato, C., Fanizzi, N., Esposito, F., Lukasiewicz, T. (2013). Representing Uncertain Concepts in Rough Description Logics via Contextual Indiscernibility Relations. In: Bobillo, F., et al. Uncertainty Reasoning for the Semantic Web II. URSW URSW URSW UniDL 2010 2009 2008 2010. Lecture Notes in Computer Science(), vol 7123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35975-0_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-35975-0_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35974-3
Online ISBN: 978-3-642-35975-0
eBook Packages: Computer ScienceComputer Science (R0)