An Algebra of Ontologies Approximation under Uncertainty
Affiliation(s)
Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria. partment of Computer Science, University of Ibadan, Ibadan, Nigeria.
Department of Mathematics, Ahmadu Bello University, Zaria, Nigeria. partment of Computer Science, University of Ibadan, Ibadan, Nigeria.
ABSTRACT
Ontologies are widely used in modeling the real world for the purpose of information sharing and reasoning. Traditional ontologies contain only concepts and relations that describe asserted facts about the world. Modeling in a dynamic world requires taking into consideration the uncertainty that may arise in the domain. In this paper, the concept of soft sets initiated by Molodtsov and the concept of rough sets introduced by Pawlack are used to define a way of instantiating ontologies of vague domains. We define ontological algebraic operations and their properties while taking into consideration the uncertain nature of domains. We show that, by doing so, intra ontological operations and their properties are preserved and formalized as operations in a vague set of objects and can be proved algebraically.
Cite this paper
Kana, A. and Akinkunmi, B. (2014) An Algebra of Ontologies Approximation under Uncertainty. International Journal of Intelligence Science, 4, 54-64. doi: 10.4236/ijis.2014.42007.
Kana, A. and Akinkunmi, B. (2014) An Algebra of Ontologies Approximation under Uncertainty. International Journal of Intelligence Science, 4, 54-64. doi: 10.4236/ijis.2014.42007.
References
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http://dx.doi.org/10.1017/CBO9780511711787 [6] Molodtsov, D. (1999) Soft Set Theory—First Results. Computers and Mathematics with Applications, 37, 19-31.
http://dx.doi.org/10.1016/S0898-1221(99)00056-5 [7] Pawlak, Z. (2002) Rough Set Theory and Its Applications. Journal of Telecommunications and Information Technology, 3, 7-10. [8] Pawlak, Z. (1982) Rough Sets. International Journal of Information and Computer Sciences, 11, 341-356.
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http://dx.doi.org/10.1016/j.ins.2006.12.008 [13] Straccia, U. (2006) A Fuzzy Description Logic for the Semantic Web. In: Sanchez, E., Ed., Fuzzy Logic and the Semantic Web, Capturing Intelligence, Elsevier, 73-90. http://dx.doi.org/10.1016/S1574-9576(06)80006-7 [14] Shafer, G. (1976) A Mathematical Theory of Evidence. Princeton University Press, Princeton. [15] Qi, G., Ji, Q., Pan, J.Z. and Du, J. (2011) Extending Description Logics with Uncertainty Reasoning in Possibilistic Logic. International Journal of Intelligent Systems, 26, 353-381. http://dx.doi.org/10.1002/int.20470 [16] Zhu, J., Qi, G. and Suntisrivaraporn, B. (2013) Tableaux Algorithms for Expressive Possibilistic Description Logics. 2013 IEEE/WIC/ACM International Joint Conferences on Web Intelligence (WI) and Intelligent Agent Technologies (IAT), Atlanta, 17-20 November 2013, 227-232. http://dx.doi.org/10.1109/wi-iat.2013.33 [17] Mitra P. and Wiederhold, G. (2004) An Ontology-Composition Algebra. International Handbooks on Information Systems, 93-117. [18] Mitra, P., Wiederhold, G. and Kersten, M. (2000) A Graph Oriented Model for Articulation of Ontology Interdependencies. Advances in Database Technology—EDBT 2000, Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 86-100. [19] Kaushik, S., Wijesekera, D. and Ammann, P. (2006) An Algebra for Composing Ontologies. Proceedings of the 2006 Conference on Formal Ontology in Information Systems, Baltimore, 9-11 November 2006, 265-276. [20] Euzenat, J. (2008) Algebras of Ontology Alignment Relations. 7th International Semantic Web Conference, Karlsruhe, 26-30 October 2008, 387-402.
[1] Bellenger, A. and Gatepaille, S. (2011) Uncertainty in Ontologies: Dempster-Shafer Theory for Data Fusion Applications. CoRR abs/1106.3876. [2] Maji, P.K., Bismas, R. and Roy, A.R. (2010) Soft Set Theory. Computers & Mathematics with Applications, 45, 555-562. http://dx.doi.org/10.1016/S0898-1221(03)00016-6 [3] Klinov, P. (2008) Pronto: A Non-Monotonic Probabilistic Description Logic Reasoner, European Semantic Web Conference. Proceedings of the Semantic Web: Research and Applications, 5th European Semantic Web Conference, Tenerife, 1-5 June 2008, 822-826. [4] Ding, Z., Peng, Y. and Pan, R. (2006) BayesOWL: Uncertainty Modeling in Semantic Web Ontologies. In: Studies in Fuzziness and Soft Computing, Soft Computing in Ontologies and Semantic Web, Springer, Berlin, Heidelberg, 3-29. [5] Baader, F., Calvanese, D., McGuinness, D., Nardi, D. and Patel-Schneider, P. (2007) The Description Logic Handbook: Theory, Implementation and Applications. 2nd Edition, Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/CBO9780511711787 [6] Molodtsov, D. (1999) Soft Set Theory—First Results. Computers and Mathematics with Applications, 37, 19-31.
http://dx.doi.org/10.1016/S0898-1221(99)00056-5 [7] Pawlak, Z. (2002) Rough Set Theory and Its Applications. Journal of Telecommunications and Information Technology, 3, 7-10. [8] Pawlak, Z. (1982) Rough Sets. International Journal of Information and Computer Sciences, 11, 341-356.
http://dx.doi.org/10.1007/BF01001956 [9] Horrocks, I. (2005) Applications of Description Logics: State of the Art and Research Challenges. In: Dau, F., Mugnier, M.-L. and Stumme, G., Eds., Conceptual Structures: Common Semantics for Sharing Knowledge, Lecture Notes in Artificial Intelligence, Springer, Berlin, Heidelberg, 78-90. [10] Krotzsch, M., Simaník, F. and Horrocks, I. (2012) A Description Logic Primer. CoRR abs/1201.4089. [11] Rudolph, S. (2011) Foundations of Description Logics. In: Polleres, A., D’Amato, C., Arenas, M., Handschuh, S., Kro- ner, P., Ossowski, S. and PatelSchneider, P.F., Eds., Reasoning Web. Semantic Technologies for the Web of Data, Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 76-136. [12] Aktas, H. and Cagman, N. (2007) Soft Sets and Soft Groups. Information Sciences, 177, 2726-2735.
http://dx.doi.org/10.1016/j.ins.2006.12.008 [13] Straccia, U. (2006) A Fuzzy Description Logic for the Semantic Web. In: Sanchez, E., Ed., Fuzzy Logic and the Semantic Web, Capturing Intelligence, Elsevier, 73-90. http://dx.doi.org/10.1016/S1574-9576(06)80006-7 [14] Shafer, G. (1976) A Mathematical Theory of Evidence. Princeton University Press, Princeton. [15] Qi, G., Ji, Q., Pan, J.Z. and Du, J. (2011) Extending Description Logics with Uncertainty Reasoning in Possibilistic Logic. International Journal of Intelligent Systems, 26, 353-381. http://dx.doi.org/10.1002/int.20470 [16] Zhu, J., Qi, G. and Suntisrivaraporn, B. (2013) Tableaux Algorithms for Expressive Possibilistic Description Logics. 2013 IEEE/WIC/ACM International Joint Conferences on Web Intelligence (WI) and Intelligent Agent Technologies (IAT), Atlanta, 17-20 November 2013, 227-232. http://dx.doi.org/10.1109/wi-iat.2013.33 [17] Mitra P. and Wiederhold, G. (2004) An Ontology-Composition Algebra. International Handbooks on Information Systems, 93-117. [18] Mitra, P., Wiederhold, G. and Kersten, M. (2000) A Graph Oriented Model for Articulation of Ontology Interdependencies. Advances in Database Technology—EDBT 2000, Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, 86-100. [19] Kaushik, S., Wijesekera, D. and Ammann, P. (2006) An Algebra for Composing Ontologies. Proceedings of the 2006 Conference on Formal Ontology in Information Systems, Baltimore, 9-11 November 2006, 265-276. [20] Euzenat, J. (2008) Algebras of Ontology Alignment Relations. 7th International Semantic Web Conference, Karlsruhe, 26-30 October 2008, 387-402.