×

Reasoning within expressive fuzzy rough description logics. (English) Zbl 1192.68662

Summary: It is generally accepted that the management of imprecision and vagueness will yield more intelligent and realistic knowledge-based applications. Description Logics (DLs) are suitable, well-known logics for managing structured knowledge that have gained considerable attention the last decade. The current research progress and the existing problems of uncertain or imprecise knowledge representation and reasoning in DLs are analyzed in this paper. An integration between the theories of fuzzy DLs and rough DLs has been attempted by providing fuzzy rough DLs based on fuzzy rough set theory. The syntax, semantics and properties of fuzzy rough DLs are given. It is proved that the satisfiability, subsumption, entailment and ABox consistency reasoning in fuzzy rough DLs may be reduced to the ABox consistency reasoning in the corresponding fuzzy DLs.

MSC:

68T27 Logic in artificial intelligence
68T37 Reasoning under uncertainty in the context of artificial intelligence
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] F. Baader, Augmenting concept language by transitive closure of roles: an alternative to terminological cycles, in: Proc. 12th Internat. Joint Conf. on Artificial Intelligence (IJCAI-91), Sydney, Australia, 1991, pp. 446-451.; F. Baader, Augmenting concept language by transitive closure of roles: an alternative to terminological cycles, in: Proc. 12th Internat. Joint Conf. on Artificial Intelligence (IJCAI-91), Sydney, Australia, 1991, pp. 446-451. · Zbl 0742.68064
[2] Baader, F.; Horrocks, I.; Sattler, U., Description logics, (Staab, S.; Studer, R., Handbook on Ontologies: International Handbooks on Information Systems (2004), Springer: Springer Berlin), 3-28
[3] Baader, F.; Nutt, W., Basic description logics, (Baader, F.; Calvanese, D.; McGuinness, D.; Nardi, D.; Patel-Schneider, P., The Description Logic Handbook: Theory, Implementation and Applications (2003), Cambridge University Press: Cambridge University Press Cambridge, MA), 47-100
[4] Baader, F.; Sattler, U., Expressive number restrictions in description logics, Journal of Logic and Computation, 9, 319-350 (1999) · Zbl 0940.03035
[5] Banerjee, M.; Pal, S. K., Roughness of a fuzzy set, Information Sciences, 93, 235-246 (1996) · Zbl 0879.04004
[6] Berardi, D.; Calvanese, D.; Giacomo, G. D., Reasoning on UML class diagrams, Artificial Intelligence, 168, 70-118 (2005) · Zbl 1132.68747
[7] F. Bobillo, M. Delgado, J. Gomez-Romero, DeLorean: a reasoner for fuzzy OWL 1.1, in: Proc. 4th Internat. Workshop on Uncertainty Reasoning for the Semantic Web (URSW 2008), Karlsruhe, Germany, October 2008.; F. Bobillo, M. Delgado, J. Gomez-Romero, DeLorean: a reasoner for fuzzy OWL 1.1, in: Proc. 4th Internat. Workshop on Uncertainty Reasoning for the Semantic Web (URSW 2008), Karlsruhe, Germany, October 2008.
[8] F. Bobillo, M. Delgado, J. Gomez-Romero, Optimizing the crisp representation of the fuzzy description logic SROIQ, in: Proc. 3rd ISWC Workshop on Uncertainty Reasoning for the Semantic Web (URSW 2007), CEUR Workshop Proceedings, Vol. 327, 2007.; F. Bobillo, M. Delgado, J. Gomez-Romero, Optimizing the crisp representation of the fuzzy description logic SROIQ, in: Proc. 3rd ISWC Workshop on Uncertainty Reasoning for the Semantic Web (URSW 2007), CEUR Workshop Proceedings, Vol. 327, 2007.
[9] F. Bobillo, M. Delgado, J. Gomez-Romero, U. Straccia, Fuzzy description logics under Gödel semantics, International Journal of Approximate Reasoning, doi:10.1016/j.ijar.2008.10.003; F. Bobillo, M. Delgado, J. Gomez-Romero, U. Straccia, Fuzzy description logics under Gödel semantics, International Journal of Approximate Reasoning, doi:10.1016/j.ijar.2008.10.003 · Zbl 1191.68647
[10] F. Bobillo, U. Straccia, FuzzyDL: an expressive fuzzy description logic reasoner, in: Proc. 17th IEEE Internat. Conf. on Fuzzy Systems (FUZZ-IEEE 2008), IEEE Computer Society, Silver Spring, MD, 2008, pp. 923-930.; F. Bobillo, U. Straccia, FuzzyDL: an expressive fuzzy description logic reasoner, in: Proc. 17th IEEE Internat. Conf. on Fuzzy Systems (FUZZ-IEEE 2008), IEEE Computer Society, Silver Spring, MD, 2008, pp. 923-930.
[11] Bonatti, P. A.; Peron, A., On the undecidability of logics with converse, nominals, recursion and counting, Artificial Intelligence, 158, 75-96 (2004) · Zbl 1085.68158
[12] Borgida, A.; Lenzerini, M.; Rosati, R., Description logics for data bases, (Baader, F.; Calvanese, D.; McGuinness, D.; Nardi, D.; Patel-Schneider, P., The Description Logic Handbook: Theory, Implementation and Applications (2003), Cambridge University Press: Cambridge University Press Cambridge), 472-494
[13] Chen, X.; Li, Q., Construction of rough approximations in fuzzy setting, Fuzzy Sets and Systems, 158, 2641-2653 (2007) · Zbl 1127.68105
[14] Chen, D.; Yang, W.; Li, F., Measures of general fuzzy rough sets on a probabilistic space, Information Sciences, 178, 3177-3187 (2008) · Zbl 1154.68526
[15] Cock, M. D.; Cornelis, C.; Kerre, E. E., Fuzzy rough sets: the forgotten step, IEEE Transactions on Fuzzy Systems, 15, 121-130 (2007)
[16] Demri, S.; Orlowska, E.; Vakarelov, D., Indiscernibility and complementarity relations in information systems, (Gerbrandy, J.; Marx, M.; de Rijke, M.; Venema, Y., FAK: Essays Dedicated to Johan van Benthem on the Occasion of his 50th Birthday (1999), Amsterdam University Press: Amsterdam University Press Amsterdam)
[17] Doherty, P.; Grabowski, M.; Lukaszewicz, W.; Szalsa, A., Towards a framework for approximate ontologies, Fundamenta Informaticae, 57, 147-165 (2003) · Zbl 1061.68154
[18] Dubois, D.; Prade, H., Rough fuzzy sets and fuzzy rough sets, International Journal of General Systems, 17, 191-209 (1990) · Zbl 0715.04006
[19] Dubois, D.; Prade, H., Putting rough sets and fuzzy sets together, (Slowinski, R., Intelligent Decision Support—Handbook of Applications and Advances of the Rough Set Theory (1992), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht), 203-232
[20] Goguen, J. A., L-fuzzy sets, Journal of Mathematical Analysis and Applications, 18, 145-174 (1967) · Zbl 0145.24404
[21] Grau, B. C.; Horrocks, I.; Motik, B.; Parsia, B.; Patel-Schneider, P.; Sattler, U., OWL 2: the next step for OWL, Journal of Web Semantics, 6, 309-322 (2008)
[22] Hajek, P., Making fuzzy description logic more general, Fuzzy Sets and Systems, 154, 1-15 (2005) · Zbl 1094.03014
[23] Hajek, P., Metamathematics of Fuzzy Logic (1998), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0937.03030
[24] Hollunder, B., An alternative proof method for possibilistic logic and its application to terminological logics, International Journal of Approximate Reasoning, 12, 85-109 (1995) · Zbl 0814.68120
[25] Horrocks, I.; Kutz, O.; Sattler, U., The even more irresistible SROIQ, (Proc. 10th Internat. Conf. of Knowledge Representation and Reasoning (KR 2006), Lake District, UK (2006), AAAI Press: AAAI Press New York), 57-67
[26] Horrocks, I.; Patel-Schneider, P. F.; Harmelen, F. V., From SHIQ and RDF to OWL: the making of a Web ontology language, Journal of Web Semantics, 1, 7-26 (2003)
[27] Horrocks, I.; Sattler, U., A description logic with transitive and inverse roles and role hierarchies, Journal of Logic and Computation, 9, 385-410 (1999) · Zbl 0940.03039
[28] Horrocks, I.; Sattler, U., Decidability of SHIQ with complex role inclusion axioms, Artificial Intelligence, 160, 79-104 (2004) · Zbl 1086.68129
[29] Horrocks, I.; Sattler, U.; Tobies, S., Practical reasoning for expressive description logics, (in: Proc. 6th Internat. Conf. on Logic for Programming and Automated Reasoning (LPAR 1999), Lecture Notes in Artificial Intelligence, Vol. 1705 (1999), Springer: Springer Berlin), 161-180 · Zbl 0947.68134
[30] Huynh, V. N.; Nakamori, Y., A roughness measure for fuzzy sets, Information Sciences, 173, 255-275 (2005) · Zbl 1074.03024
[31] Jaeger, M., Probabilistic reasoning in terminological logics, (Doyle, J.; Sandewall, E.; Torasso, P., Proc. 4th Internat. Conf. on Principles of Knowledge Representation and Reasoning (KR 1994) (1994), Morgan Kaufmann Publishers: Morgan Kaufmann Publishers Los Altos, CA), 305-316
[32] Jensen, R.; Shen, Q., Fuzzy rough sets assisted attribute selection, IEEE Transactions on Fuzzy Systems, 15, 73-89 (2007)
[33] Jiang, Y.; Shi, Z.; Tang, Y.; Wang, J., Fuzzy description logic for semantics representation of the semantic Web, Journal of Software, 18, 1257-1269 (2007) · Zbl 1174.68448
[34] Jiang, Y.; Wang, J.; Tang, S.; Xiao, B., Reasoning with rough description logics: an approximate concepts approach, Information Sciences, 179, 600-612 (2009) · Zbl 1170.68037
[35] M.C.A. Klein, P. Mika, S. Schlobach, Approximate instance unification using RoughOWL: querying with similarity in open academia, in: F. Bobillo, P.C.G. Costa, C.D. Amato, et al. (Eds.), Proc. 3rd Workshop on Uncertainty Reasoning for the Semantic Web, CEUR Workshop Proceedings, CEUR-WS.org, 2007.; M.C.A. Klein, P. Mika, S. Schlobach, Approximate instance unification using RoughOWL: querying with similarity in open academia, in: F. Bobillo, P.C.G. Costa, C.D. Amato, et al. (Eds.), Proc. 3rd Workshop on Uncertainty Reasoning for the Semantic Web, CEUR Workshop Proceedings, CEUR-WS.org, 2007.
[36] Klement, E. P.; Mesiar, R.; Pap, E., Triangular norms, Position paper I: basic analytical and algebraic properties, Fuzzy Sets and Systems, 143, 5-26 (2004) · Zbl 1038.03027
[37] Klir, G. J.; Yuan, B., Fuzzy Sets and Fuzzy Logic: Theory and Applications (1995), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0915.03001
[38] Li, T., Rough approximation operators on two universes of discourse and their fuzzy extensions, Fuzzy Sets and Systems, 159, 3033-3050 (2008) · Zbl 1176.03036
[39] Li, Y.; Xu, B.; Lu, J.; Kang, D., On computational complexity of the extended fuzzy description logic with numerical restriction, Journal of Software, 17, 968-975 (2006) · Zbl 1101.68867
[40] Y. Li, B. Xu, J. Lu, D. Kang, Discrete tableau algorithms for FSHI, in: Proc. Internat. Workshop on Description Logics (DL 2006), Lake District, UK, 2006.; Y. Li, B. Xu, J. Lu, D. Kang, Discrete tableau algorithms for FSHI, in: Proc. Internat. Workshop on Description Logics (DL 2006), Lake District, UK, 2006.
[41] Liang, H., The Ministry of Health of the People’s Republic of China: clinic diagnosis criteria for severe acute respiratory syndrome, The Chinese Journal of Clinical Pharmacology, 19, 200 (2003)
[42] Liau, C. J., On rough terminological logics, (Tsumoto, S.; Kobayashi, S.; Yokomori, T.; Tanaka, H.; Nakamura, A., Proc. 4th Internat. Workshop on Rough Sets, Fuzzy Sets, and Machine Discovery (1996), Tokyo University Press), 47-54
[43] Liu, G., Generalized rough sets over lattices, Information Sciences, 178, 1651-1662 (2008) · Zbl 1136.03328
[44] Lukasiewicz, T., Expressive probabilistic description logics, Artificial Intelligence, 172, 852-883 (2008) · Zbl 1182.68283
[45] Lukasiewicz, T.; Straccia, U., Managing uncertainty and vagueness in description logics for the semantic Web, Journal of Web Semantics, 6, 291-308 (2008)
[46] Lutz, C., NEXP TIME-complete description logics with concrete domains, ACM Transactions on Computational Logic, 5, 669-705 (2004) · Zbl 1367.68288
[47] Lutz, C.; Areces, C.; Horrocks, I.; Sattler, U., Keys, nominals, and concrete domains, Journal of Artificial Intelligence Research, 23, 667-726 (2005) · Zbl 1080.68683
[48] Nebel, B., Terminological reasoning is inherently intractable, Artificial Intelligence, 43, 235-249 (1990) · Zbl 0717.68089
[49] Orlowska, E., Kripke semantics for knowledge representation logics, Studia Logica, 49, 255-272 (1990) · Zbl 0726.03023
[50] Pawlak, Z., Rough sets, International Journal of Computer and Information Sciences, 11, 341-356 (1982) · Zbl 0501.68053
[51] Pawlak, Z., Rough Sets: Theoretical Aspects of Reasoning about Data (1991), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0758.68054
[52] Pei, D. W., A generalized model of fuzzy rough sets, International Journal of General Systems, 34, 603-613 (2005) · Zbl 1082.03047
[53] Qi, G.; Pan, J. Z.; Ji, Q., Extending description logics with uncertainty reasoning in possibilistic logic, (Mellouli, K., Proc. of European Conf. on Symbolic and Quantitative Approaches to Reasoning with Uncertainty (ECSQARU 2007), Lecture Notes in Computer Science, Vol. 4724 (2007), Springer: Springer Berlin), 828-839 · Zbl 1148.68535
[54] Schlobach, S.; Klein, M.; Peelen, L., Description logics with approximate definitions: precise modeling of vague concepts, (Veloso, M. M., Proc. 20th Internat. Joint Conf. on Artificial Intelligence (IJCAI 2007) (2007), AAAI Press: AAAI Press New York), 557-562
[55] Schmidt-Schauß, M.; Smolka, G., Attributive concept descriptions with complements, Artificial Intelligence, 48, 1-26 (1991) · Zbl 0712.68095
[56] Shi, Z.; Dong, M.; Jiang, Y.; Zhang, H., A logic foundation for the semantic Web, Science in China, Series F Information Sciences, 48, 161-178 (2005)
[57] Sirin, E.; Parsia, B.; Grau, B. C.; Kalyanpur, A.; Katz, Y., Pellet: a practical OWL-DL reasoner, Journal of Web Semantics, 5, 51-53 (2007)
[58] 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) · Zbl 1182.68292
[59] Stoilos, G.; Straccia, U.; Stamou, G.; Pan, J. Z., General concept inclusions in fuzzy description logics, (Proc. 17th European Conf. on Artificial Intelligence (ECAI 2006) (2006), IOS Press), 457-461
[60] Straccia, U., Reasoning within fuzzy description logics, Journal of Artificial Intelligence Research, 14, 137-166 (2001) · Zbl 0973.03034
[61] Straccia, U., Description logics over lattices, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 14, 1-16 (2006) · Zbl 1093.68107
[62] Straccia, U., A fuzzy description logic for the semantic Web, (Sanchez, E., Capturing Intelligence: Fuzzy Logic and the Semantic Web (2006), Elsevier Science Publishers: Elsevier Science Publishers Amsterdam), 73-90
[63] Straccia, U., Description logics with fuzzy concrete domains, (Proc. 21st Conf. in Uncertainty in Artificial Intelligence (UAI 2005) (2005), AUAI Press), 559-567
[64] Tho, Q. T.; Hui, S. C.; Fong, A. C.M.; Cao, T. H., Automatic fuzzy ontology generation for semantic Web, IEEE Transactions on Knowledge and Data Engineering, 18, 842-856 (2006)
[65] Tobies, S., The complexity of reasoning with cardinality restrictions and nominals in expressive description logics, Journal of Artificial Intelligence Research, 12, 199-217 (2000) · Zbl 0941.03029
[66] Tsarkov, D.; Horrocks, I., FaCT++ description logic reasoner: system description, (Proc. 3rd Internat. Joint Conf. on Automated Reasoning (IJCAR 2006) (2006), Springer: Springer Berlin), 292-297
[67] Wu, W.; Mi, J.; Zhang, W., Generalized fuzzy rough sets, Information Sciences, 151, 263-282 (2003) · Zbl 1019.03037
[68] Xu, W.; Zhang, W., Measuring roughness of generalized rough sets induced by a covering, Fuzzy Sets and Systems, 158, 2443-2455 (2007) · Zbl 1127.68106
[69] Yao, Y. Y., Probabilistic rough set approximations, International Journal of Approximate Reasoning, 49, 255-271 (2008) · Zbl 1191.68702
[70] Yen, J., Generalizing term subsumption languages to fuzzy logic, (Proc. 12th Internat. Joint Conf. on Artificial Intelligence (IJCAI-91) (1991), Morgan Kaufmann Publishers: Morgan Kaufmann Publishers Los Altos, CA), 472-477 · Zbl 0742.68062
[71] Yeung, D. S.; Chen, D.; Tsang, E. C.C.; Lee, J. W.T.; Wang, X., On the generalization of fuzzy rough sets, IEEE Transactions on Fuzzy Systems, 13, 343-361 (2005)
[72] Zadeh, L. A., Fuzzy sets, Information and Control, 8, 338-353 (1965) · Zbl 0139.24606
[73] Ziarko, W., Probabilistic approach to rough sets, International Journal of Approximate Reasoning, 4, 272-284 (2008) · Zbl 1191.68705
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.