Abstract
The aim of this talk is to present a detailed, self-contained and comprehensive account of the state of the art in representing and reasoning with structured fuzzy knowledge. Fuzzy knowledge comes into play whenever one has to deal with concepts for which membership is a matter of degree (e.g., the degree of illness is a function of, among others, the body temperature). Specifically, we address the case of the fuzzy variants of conceptual languages of the OWL 2 family.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
More concretely, the intensity of precipitation is expressed in terms of a precipitation rate R: volume flux of precipitation through a horizontal surface, i.e. \(m^3/ m^2 s = m s^{-1}\). It is usually expressed in mm / h.
- 2.
- 3.
The function \(\mathcal {I} _{x}^{a}\) is as \(\mathcal {I} \) except that x is interpreted as a.
References
Agarwal, S., Lamparter, S.: Smart: a semantic matchmaking portal for electronic markets. In: CEC 2005: Proceedings of the Seventh IEEE International Conference on E-Commerce Technology (CEC 2005), pp. 405–408. IEEE Computer Society, Washington (2005)
Andreasen, T., Bulskov, H.: Conceptual querying through ontologies. Fuzzy Sets Syst. 160(15), 2159–2172 (2009)
Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)
Baader, F., Peñaloza, R.: Are fuzzy description logics with general concept inclusion axioms decidable? In: Proceedings of 2011 IEEE International Conference on Fuzzy Systems (Fuzz-IEEE 2011). IEEE Press (2011)
Baader, F., Peñaloza, R.: GCIs make reasoning in fuzzy DLs with the product T-norm undecidable. In: Proceedings of the 24th International Workshop on Description Logics (DL-11). CEUR Electronic Workshop Proceedings (2011)
Balaj, R., Groza, A.: Detecting influenza epidemics based on real-time semantic analysis of Twitter streams. In: Proceedings of the 3rd International Conference on Modelling and Development of Intelligent Systems (MDIS 2013), pp. 30–39 (2013)
Bobillo, F., Bou, F., Straccia, U.: On the failure of the finite model property in some fuzzy description logics. Fuzzy Sets Syst. 172(1), 1–12 (2011)
Bobillo, F., Delgado, M., Gómez-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-06), November 2006
Bobillo, F., Delgado, M., Gómez-Romero, J.: A crisp representation for fuzzy \(\cal SHOIN\) with fuzzy nominals and general concept inclusions. In: da Costa, P.C.G., d’Amato, C., Fanizzi, N., Laskey, K.B., Laskey, K.J., Lukasiewicz, T., Nickles, M., Pool, M. (eds.) URSW 2005–2007. LNCS (LNAI), vol. 5327, pp. 174–188. Springer, Heidelberg (2008)
Bobillo, F., Delgado, M., Gómez-Romero, J.: Delorean: a reasoner for fuzzy OWL 1.1. In: Proceedings of the 4th International Workshop on Uncertainty Reasoning for the Semantic Web (URSW 2008), October 2008, vol. 423. CEUR Workshop Proceedings (2008)
Bobillo, F., Delgado, M., Gómez-Romero, J.: Optimizing the crisp representation of the fuzzy description logic \(\cal \cal SROIQ\cal \). In: da Costa, P.C.G., d’Amato, C., Fanizzi, N., Laskey, K.B., Laskey, K.J., Lukasiewicz, T., Nickles, M., Pool, M. (eds.) URSW 2005–2007. LNCS (LNAI), vol. 5327, pp. 189–206. Springer, Heidelberg (2008)
Bobillo, F., Delgado, M., Gómez-Romero, J., Straccia, U.: Fuzzy description logics under Gödel semantics. Int. J. Approx. Reason. 50(3), 494–514 (2009)
Bobillo, F., Straccia, U.: A fuzzy description logic with product T-norm. In: Proceedings of the IEEE International Conference on Fuzzy Systems (Fuzz-IEEE-07), pp. 652–657. IEEE Computer Society (2007)
Bobillo, F., Straccia, U.: fuzzyDL: an expressive fuzzy description logic reasoner. In: 2008 International Conference on Fuzzy Systems (FUZZ-08), pp. 923–930. IEEE Computer Society (2008)
Bobillo, F., Straccia, U.: On qualified cardinality restrictions in fuzzy description logics under Łukasiewicz semantics. In: Magdalena, L., Ojeda-Aciego, M., Luis Verdegay, J. (eds.) Proceedings of the 12th International Conference of Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2008), June 2008, pp. 1008–1015 (2008)
Bobillo, F., Straccia, U.: Towards a crisp representation of fuzzy description logics under Łukasiewicz semantics. In: An, A., Matwin, S., Raś, Z.W., Ślzak, D. (eds.) Foundations of Intelligent Systems. LNCS (LNAI), vol. 4994, pp. 309–318. Springer, Heidelberg (2008)
Bobillo, F., Straccia, U.: Extending datatype restrictions in fuzzy description logics. In: Proceedings of the 9th International Conference on Intelligent Systems Design and Applications (ISDA-09), pp. 785–790. IEEE Computer Society (2009)
Bobillo, F., Straccia, U.: Fuzzy description logics with fuzzy truth values. In: Carvalho, J.P.B., Dubois, D., Kaymak, U., Sousa, J.M.C. (eds.) Proceedings of the 13th World Congress of the International Fuzzy Systems Association and 6th Conference of the European Society for Fuzzy Logic and Technology (IFSA-EUSFLAT 2009), July 2009, pp. 189–194 (2009)
Bobillo, F., Straccia, U.: Fuzzy description logics with general T-norms and datatypes. Fuzzy Sets Syst. 160(23), 3382–3402 (2009)
Bobillo, F., Straccia, U.: An OWL ontology for fuzzy OWL 2. In: Rauch, J., Raś, Z.W., Berka, P., Elomaa, T. (eds.) ISMIS 2009. LNCS, vol. 5722, pp. 151–160. Springer, Heidelberg (2009)
Bobillo, F., Straccia, U.: Supporting fuzzy rough sets in fuzzy description logics. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS, vol. 5590, pp. 676–687. Springer, Heidelberg (2009)
Bobillo, F., Straccia, U.: Representing fuzzy ontologies in OWL 2. In: Proceedings of the 19th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2010), July 2010, pp. 2695–2700. IEEE Press (2010)
Bobillo, F., Straccia, U.: Aggregation operators and fuzzy OWL 2. In: Proceedings of the 20th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011), June 2011, pp. 1727–1734. IEEE Press (2011)
Bobillo, F., Straccia, U.: Fuzzy ontologies and fuzzy integrals. In: Proceedings of the 11th International Conference on Intelligent Systems Design and Applications (ISDA 2011), November 2011, pp. 1311–1316. IEEE Press (2011)
Bobillo, F., Straccia, U.: Fuzzy ontology representation using OWL 2. Int. J. Approx. Reason. 52, 1073–1094 (2011)
Bobillo, F., Straccia, U.: On partitioning-based optimisations in expressive fuzzy description logics. In: Proceedings of the 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2015), 2–5 August 2015. IEEE Press (2015)
Bobillo, F., Straccia, U.: Optimising fuzzy description logic reasoners with general concept inclusions absorption. Fuzzy Sets Syst. http://www.sciencedirect.com/science/article/pii/S0165011414004850
Bonatti, P.A., Tettamanzi, A.G.B.: Some complexity results on fuzzy description logics. In: Di Gesú, V., Masulli, F., Petrosino, A. (eds.) WILF 2003. LNCS (LNAI), vol. 2955, pp. 19–24. Springer, Heidelberg (2006)
Borgwardt, S., Distel, F., Peñaloza, R.: How fuzzy is my fuzzy description logic? In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 82–96. Springer, Heidelberg (2012)
Borgwardt, S., Distel, F., Peñaloza, R.: Non-Gödel negation makes unwitnessed consistency undecidable. In: Proceedings of the 2012 International Workshop on Description Logics (DL-2012), vol. 846. CEUR-WS.org (2012)
Borgwardt, S., Peñaloza, R.: Description logics over lattices with multi-valued ontologies. In: Proceedings of the Twenty-Second International Joint Conference on Artificial Intelligence (IJCAI-11), pp. 768–773 (2011)
Borgwardt, S., Peñaloza, R.: Finite lattices do not make reasoning in \({\cal ALCI}\) harder. In: Proceedings of the 7th International Workshop on Uncertainty Reasoning for the Semantic Web (URSW-11), vol. 778, pp. 51–62. CEUR-WS.org (2011)
Borgwardt, S., Peñaloza, R.: Fuzzy ontologies over lattices with T-norms. In: Proceedings of the 24th International Workshop on Description Logics (DL-11). CEUR Electronic Workshop Proceedings (2011)
Borgwardt, S., Peñaloza, R.: A tableau algorithm for fuzzy description logics over residuated de morgan lattices. In: Krötzsch, M., Straccia, U. (eds.) RR 2012. LNCS, vol. 7497, pp. 9–24. Springer, Heidelberg (2012)
Borgwardt, S., Peñaloza, R.: Undecidability of fuzzy description logics. In: Proceedings of the 13th International Conference on Principles of Knowledge Representation and Reasoning (KR-12), pp. 232–242. AAAI Press, Rome (2012)
Bou, F., Cerami, M., Esteva, F.: Finite-valued Łukasiewicz modal logic is PSPACE-complete. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI-11), pp. 774–779 (2011)
Calegari, S., Sanchez, E.: Object-fuzzy concept network: an enrichment of ontologies in semantic information retrieval. J. Am. Soc. Inf. Sci. Technol. 59(13), 2171–2185 (2008)
Carlsson, C., Brunelli, M., Mezei, J.: Decision making with a fuzzy ontology. Soft Comput. 16(7), 1143–1152 (2012)
Cerami, M., Esteva, F., Bou, F.: Decidability of a description logic over infinite-valued product logic. In: Proceedings of the Twelfth International Conference on Principles of Knowledge Representation and Reasoning (KR-10). AAAI Press (2010)
Cerami, M., Straccia, U.: On the undecidability of fuzzy description logics with GCIs with Lukasiewicz T-norm. Technical report, Computing Research Repository (2011). Available as CoRR technical report at http://arxiv.org/abs/1107.4212
Cerami, M., Straccia, U.: Undecidability of KB satisfiability for ł-\({\cal ALC}\) with GCIs. Unpublished manuscript, July 2011
Chen, R.-C., Bau, C.T., Yeh, C.-J.: Merging domain ontologies based on the WordNet system and fuzzy formal concept analysis techniques. Appl. Soft Comput. 11(2), 1908–1923 (2011)
Colucci, S., Di Noia, T., Ragone, A., Ruta, M., Straccia, U., Tinelli, E.: Informative Top-k retrieval for advanced skill management. In: de Virgilio, R., Giunchiglia, F., Tanca, L. (eds.) Semantic Web Information Management, Chap. 19. Springer, Heidelberg (2010)
Costa, P.C.G., Laskey, K.B., Lukasiewicz, T.: Uncertainty representation and reasoning in the semantic web. In: Semantic Web Engineering in the Knowledge Society, pp. 315–340. IGI Global (2008)
Cuenca-Grau, B., Horrocks, I., Motik, B., Parsia, B., Patel-Schneider, P.F., Sattler, U.: OWL 2: the next step for OWL. J. Web Seman. 6(4), 309–322 (2008)
d’Aquin, M., Lieber, J., Napoli, A.: Towards a semantic portal for oncology using a description logic with fuzzy concrete domains. In: Sanchez, E. (ed.) Fuzzy Logic and the Semantic Web, Capturing Intelligence, pp. 379–393. Elsevier, New York (2006)
Dasiopoulou, S., Kompatsiaris, I.: Trends and issues in description logics frameworks for image interpretation. In: Konstantopoulos, S., Perantonis, S., Karkaletsis, V., Spyropoulos, C.D., Vouros, G. (eds.) SETN 2010. LNCS, vol. 6040, pp. 61–70. Springer, Heidelberg (2010)
Dasiopoulou, S., Kompatsiaris, I., Strintzis, M.G.: Applying fuzzy DLs in the extraction of image semantics. J. Data Seman. 14, 105–132 (2009)
Dasiopoulou, S., Kompatsiaris, I., Strintzis, M.G.: Investigating fuzzy DLs-based reasoning in semantic image analysis. Multimed. Tools Appl. 49(1), 167–194 (2010)
Díaz-Rodríguez, N., León-Cadahía, O., Pegalajar-Cuéllar, M., Lilius, J., Delgado, M.: Handling real-world context-awareness, uncertainty and vagueness in real-time human activity tracking and recognition with a fuzzy ontology-based hybrid method. Sensors 14(10), 18131–18171 (2014)
Díaz-Rodríguez, N., Pegalajar-Cuéllar, M., Lilius, J., Delgado, M.: A fuzzy ontology for semantic modelling and recognition of human behaviour. Knowl.-Based Syst. 66, 46–60 (2014)
Dinh-Khac, D., Hölldobler, S., Tran, D.-K.: The fuzzy linguistic description logic \({\cal ALC}_{FL}\). In: Proceedings of the 11th International Conference on Information Processing and Managment of Uncertainty in Knowledge-Based Systems. IPMU-06, pp. 2096–2103. E.D.K, Paris (2006)
Dubois, D., Mengin, J., Prade, H.: Possibilistic uncertainty and fuzzy features in description logic. A preliminary discussion. In: Sanchez, E. (ed.) Capturing Intelligence: Fuzzy Logic and the Semantic Web. Elsevier, New York (2006)
Dubois, D., Prade, H.: Fuzzy Sets and Systems. Academic Press, Orlando (1980)
Dubois, D., Prade, H.: Can we enforce full compositionality in uncertainty calculi? In: Proceedings of the 12th National Conference on Artificial Intelligence (AAAI-94), Seattle, Washington, pp. 149–154 (1994)
Dubois, D., Prade, H.: Possibility theory, probability theory and multiple-valued logics: a clarification. Ann. Math. Artif. Intel. 32(1–4), 35–66 (2001)
Eich, M., Hartanto, R., Kasperski, S., Natarajan, S., Wollenberg, J.: Towards coordinated multirobot missions for lunar sample collection in an unknown environment. J. Field Robot. 31(1), 35–74 (2014)
Eich, T.: An application of fuzzy DL-based semantic perception to soil container classification. In: IEEE International Conference on Technologies for Practical Robot Applications (TePRA-13), pp. 1–6. IEEE Press (2013)
Fernández, C.: Understanding image sequences: the role of ontologies in cognitive vision systems. Ph.D. thesis, Universitat Autònoma de Barcelona, Spain (2010)
fuzzyDL. http://www.straccia.info/software/fuzzyDL/fuzzyDL.html
Fuzzy OWL 2 web ontology language (2011). ISTI - CNR. http://www.straccia.info/software/FuzzyOWL/
Gao, M., Liu, C.: Extending OWL by fuzzy description logic. In: Proceedings of the 17th IEEE International Conference on Tools with Artificial Intelligence (ICTAI-05), pp. 562–567. IEEE Computer Society, Washington (2005)
Haarslev, V., Pai, H.-I., Shiri, N.: Optimizing tableau reasoning in ALC extended with uncertainty. In: Proceedings of the 2007 International Workshop on Description Logics (DL-07) (2007)
Habiballa, H.: Resolution strategies for fuzzy description logic. In: Proceedings of the 5th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-07), vol. 2, pp. 27–36 (2007)
Hähnle, R.: Advanced many-valued logics. In: Gabbay, D.M., Guenthner, F. (eds.) Handbook of Philosophical Logic, vol. 2, 2nd edn. Kluwer, Dordrecht (2001)
Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)
Hájek, P.: Making fuzzy description logics more general. Fuzzy Sets Syst. 154(1), 1–15 (2005)
Hájek, P.: What does mathematical fuzzy logic offer to description logic? In: Sanchez, E. (ed.) Fuzzy Logic and the Semantic Web, Capturing Intelligence, Chap. 5, pp. 91–100. Elsevier, New York (2006)
Hájek, P.: On witnessed models in fuzzy logic. Math. Logic Q. 53(1), 66–77 (2007)
Hölldobler, S., Khang, T.D., Störr, H.-P.: A fuzzy description logic with hedges as concept modifiers. In: Phuong, N.H., Nguyen, H.T., Ho, N.C., Santiprabhob, P. (eds.) Proceedings InTech/VJFuzzy’2002, pp. 25–34. Institute of Information Technology, Vietnam Center for Natural Science and Technology, Science and Technics Publishing House, Hanoi (2002)
Hölldobler, S., Nga, N.H., Khang, T.D.: The fuzzy description logic \({\cal ALC}_{FH}\). In: Proceeedings of the International Workshop on Description Logics (DL-05) (2005)
Hölldobler, S., Störr, H.-P., Khang, T.D.: The fuzzy description logic \(\cal ALC_{FH}\) with hedge algebras as concept modifiers. J. Adv. Comput. Intel. 7(3), 294–305 (2003)
Hölldobler, S., Störr, H.-P., Khang, T.D.: A fuzzy description logic with hedges and concept modifiers. In: Proceedings of the 10th International Conference on Information Processing and Managment of Uncertainty in Knowledge-Based Systems, IPMU-04 (2004)
Hölldobler, S., Störr, H.-P., Khang, T.D.: The subsumption problem of the fuzzy description logic \({\cal ALC}_{FH}\). In: Proceedings of the 10th International Conference on Information Processing and Managment of Uncertainty in Knowledge-Based Systems (IPMU-04) (2004)
Iglesias, J., Lehmann, J.: Towards integrating fuzzy logic capabilities into an ontology-based inductive logic programming framework. In: Proceedings of the 11th International Conference on Intelligent Systems Design and Applications (ISDA 2011), pp. 1323–1328 (2011)
Jiang, Y., Liu, H., Tang, Y., Chen, Q.: Semantic decision making using ontology-based soft sets. Math. Comput. Model. 53(5–6), 1140–1149 (2011)
Jiang, Y., Tang, Y., Chen, Q., Wang, J., Tang, S.: Extending soft sets with description logics. Comput. Math. Appl. 59(6), 2087–2096 (2010)
Jiang, Y., Yong Tang, J., Wang, P.D., Tang, S.: Expressive fuzzy description logics over lattices. Knowl.-Based Syst. 23, 150–161 (2010)
Jiang, Y., Tang, Y., Wang, J., Tang, S.: Reasoning within intuitionistic fuzzy rough description logics. Inf. Sci. 179, 2362–2378 (2009)
Jiang, Y., Tang, Y., Wang, J., Tang, S.: Representation and reasoning of context-dependant knowledge in distributed fuzzy ontologies. Expert Syst. Appl. 37(8), 6052–6060 (2010)
Jiang, Y., Wang, J., Deng, P., Tang, S.: Reasoning within expressive fuzzy rough description logics. Fuzzy Sets Syst. 160(23), 3403–3424 (2009)
Yuncheng Jiang, J., Wang, S.T., Xiao, B.: Reasoning with rough description logics: an approximate concepts approach. Inf. Sci. 179(5), 600–612 (2009)
Kang, D., Xu, B., Lu, J., Li, Y.: Reasoning for a fuzzy description logic with comparison expressions. In: Proceeedings of the International Workshop on Description Logics (DL-06). CEUR Workshop Proceedings (2006)
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Trends in Logic - Studia Logica Library. Kluwer Academic Publishers, Dordrecht (2000)
Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall Inc., Upper Saddle River (1995)
Konstantopoulos, S., Apostolikas, G.: Fuzzy-DL reasoning over unknown fuzzy degrees. In: Meersman, R., Tari, Z. (eds.) OTM-WS 2007, Part II. LNCS, vol. 4806, pp. 1312–1318. Springer, Heidelberg (2007)
Konstantopoulos, S., Karkaletsis, V., Bilidas, D.: An intelligent authoring environment for abstract semantic representations of cultural object descriptions. In: Proceedings of the EACL 2009 Workshop on Language Technology and Resources for Cultural Heritage, Social Sciences, Humanities, and Education (LaTeCHSHELT&R 2009), pp. 10–17 (2009)
Lee, C.-S., Jian, Z.-W., Huang, L.-K.: A fuzzy ontology and its application to news summarization. IEEE Trans. Syst. Man Cybern. Part B 35(5), 859–880 (2005)
Lee, C.-S., Wang, M.H., Hagras, H.: A Type-2 fuzzy ontology and its application to personal diabetic-diet recommendation. IEEE Trans. Fuzzy Syst. 18(2), 374–395 (2010)
Letia, I.A., Groza, A.: Modelling imprecise arguments in description logic. Adv. Electr. Comput. Eng. 9(3), 94–99 (2009)
Lisi, F.A., Straccia, U.: A logic-based computational method for the automated induction of fuzzy ontology axioms. Fundamenta Informaticae 124(4), 503–519 (2013)
Lisi, F.A., Straccia, U.: A system for learning GCI axioms in fuzzy description logics. In: Proceedings of the 26th International Workshop on Description Logics (DL-13). CEUR Workshop Proceedings, vol. 1014, pp. 760–778. CEUR-WS.org (2013)
Lisi, F.A., Straccia, U.: Can ILP deal with incomplete and vague structured knowledge? In: Muggleton, S.H., Watanabe, H. (eds.) Latest Advances in Inductive Logic Programming, Chap. 21, pp. 199–206. World Scientific, Singapore (2014)
Lisi, F.A., Straccia, U.: Learning in description logics with fuzzy concrete domains. Fundamenta Informaticae in press
Lisi, F.A., Straccia, U.: An inductive logic programming approach to learning inclusion axioms in fuzzy description logics. In: 26th Italian Conference on Computational Logic (CILC-11). CEUR Electronic Workshop Proceedings, vol. 810, pp. 57–71 (2011)
Lisi, F.A., Straccia, U.: Towards learning fuzzy DL inclusion axioms. In: Petrosino, A. (ed.) WILF 2011. LNCS, vol. 6857, pp. 58–66. Springer, Heidelberg (2011)
Lisi, F.A., Straccia, U.: Dealing with incompleteness and vagueness in inductive logic programming. In: 28th Italian Conference on Computational Logic (CILC-13). CEUR Electronic Workshop Proceedings, vol. 1068, pp. 179–193 (2013)
Lisi, F.A., Straccia, U.: A FOIL-like method for learning under incompleteness and vagueness. In: Zaverucha, G., Santos Costa, V., Paes, A. (eds.) ILP 2013. LNCS, vol. 8812, pp. 123–139. Springer, Heidelberg (2014)
Liu, C., Liu, D., Wang, S.: Situation modeling and identifying under uncertainty. In: Proceedings of the 2nd Pacific-Asia Conference on Circuits, Communications and System (PACCS 2010), pp. 296–299 (2010)
Liu, C., Liu, D., Wang, S.: Fuzzy geospatial information modeling in geospatial semantic retrieval. Adv. Math. Comput. Meth. 2(4), 47–53 (2012)
Liu, O., Tian, Q., Ma, J.: A fuzzy description logic approach to model management in R&D project selection. In: Proceedings of the 8th Pacific Asia Conference on Information Systems (PACIS-04) (2004)
Lukasiewicz, T.: Fuzzy description logic programs under the answer set semantics for the semantic web. In: Second International Conference on Rules and Rule Markup Languages for the Semantic Web (RuleML-06), pp. 89–96. IEEE Computer Society (2006)
Lukasiewicz, T.: Fuzzy description logic programs under the answer set semantics for the semantic web. Fundamenta Informaticae 82(3), 289–310 (2008)
Lukasiewicz, T., Straccia, U.: Description logic programs under probabilistic uncertainty and fuzzy vagueness. In: Mellouli, K. (ed.) ECSQARU 2007. LNCS (LNAI), vol. 4724, pp. 187–198. Springer, Heidelberg (2007)
Lukasiewicz, T., Straccia, U.: Tightly integrated fuzzy description logic programs under the answer set semantics for the semantic web. In: Marchiori, M., Pan, J.Z., Marie, C.S. (eds.) RR 2007. LNCS, vol. 4524, pp. 289–298. Springer, Heidelberg (2007)
Lukasiewicz, T., Straccia, U.: Top-k retrieval in description logic programs under vagueness for the semantic web. In: Prade, H., Subrahmanian, V.S. (eds.) SUM 2007. LNCS (LNAI), vol. 4772, pp. 16–30. Springer, Heidelberg (2007)
Lukasiewicz, T., Straccia, U.: Managing uncertainty and vagueness in description logics for the semantic web. J. Web Seman. 6, 291–308 (2008)
Lukasiewicz, T., Straccia, U.: Tightly coupled fuzzy description logic programs under the answer set semantics for the semantic web. Int. J. Seman. Web Inf. Syst. 4(3), 68–89 (2008)
Lukasiewicz, T., Straccia, U.: Description logic programs under probabilistic uncertainty and fuzzy vagueness. Int. J. Approx. Reason. 50(6), 837–853 (2009)
Mailis, T., Stoilos, G., Stamou, G.: Expressive reasoning with horn rules and fuzzy description logics. In: Marchiori, M., Pan, J.Z., Marie, C.S. (eds.) RR 2007. LNCS, vol. 4524, pp. 43–57. Springer, Heidelberg (2007)
Martínez-Cruz, C., van der Heide, A., Sánchez, D., Triviño, G.: An approximation to the computational theory of perceptions using ontologies. Expert Syst. Appl. 39(10), 9494–9503 (2012)
Meghini, C., Sebastiani, F., Straccia, U.: A model of multimedia information retrieval. J. ACM 48(5), 909–970 (2001)
Mostert, P.S., Shields, A.L.: On the structure of semigroups on a compact manifold with boundary. Ann. Math. 65, 117–143 (1957)
OWL web ontology language overview. W3C (2004). http://www.w3.org/TR/owl-features/
OWL 2 web ontology language document overview. W3C (2009). http://www.w3.org/TR/2009/REC-owl2-overview-20091027/
Pan, J.Z., Stamou, G., Stoilos, G., Thomas, E.: Expressive querying over fuzzy DL-Lite ontologies. In: Twentieth International Workshop on Description Logics (2007)
Pérez, I.J., Wikström, R., Mezei, J., Carlsson, C., Herrera-Viedma, E.: A new consensus model for group decision making using fuzzy ontology. Soft Comput. 17(9), 1617–1627 (2013)
Quan, T.T., Hui, S.C., Fong, A.C.M., Cao, T.H.: Automatic fuzzy ontology generation for semantic help-desk support. IEEE Trans. Ind. Inf. 2(3), 155–164 (2006)
Quan, T.T., Hui, S.C., Fong, A.C.M., Cao, T.H.: Automatic fuzzy ontology generation for semantic web. IEEE Trans. Knowl. Data Eng. 18(6), 842–856 (2006)
Ragone, A., Straccia, U., Bobillo, F., Di Noia, T., Di Sciascio, E.: Fuzzy bilateral matchmaking in e-marketplaces. In: Lovrek, I., Howlett, R.J., Jain, L.C. (eds.) KES 2008, Part III. LNCS (LNAI), vol. 5179, pp. 293–301. Springer, Heidelberg (2008)
Ragone, A., Straccia, U., Di Noia, T., Di Sciascio, E., Donini, F.M.: Extending datalog for matchmaking in P2P e-marketplaces. In: Ceci, M., Malerba, D., Tanca, L. (eds.) 15th Italian Symposium on Advanced Database Systems (SEBD-07), pp. 463–470 (2007)
Ragone, A., Straccia, U., Di Noia, T., Di Sciascio, E., Donini, F.M.: Vague knowledge bases for matchmaking in P2P e-marketplaces. In: Franconi, E., Kifer, M., May, W. (eds.) ESWC 2007. LNCS, vol. 4519, pp. 414–428. Springer, Heidelberg (2007)
Ragone, A., Straccia, U., Di Noia, T., Di Sciascio, E., Donini, F.M.: Towards a fuzzy logic for automated multi-issue negotiation. In: Hartmann, S., Kern-Isberner, G. (eds.) FoIKS 2008. LNCS, vol. 4932, pp. 381–396. Springer, Heidelberg (2008)
Ragone, A., Straccia, U., Di Noia, T., Di Sciascio, E., Donini, F.M.: Fuzzy matchmaking in e-marketplaces of peer entities using datalog. Fuzzy Sets Syst. 160(2), 251–268 (2009)
Rodger, J.A.: A fuzzy linguistic ontology payoff method for aerospace real options valuation. Expert Syst. Appl. 40(8), 2828–2840 (2013)
Rodríguez, N.D., Cuéllar, M.P., Lilius, J., Calvo-Flores, M.D.: A survey on ontologies for human behavior recognition. ACM Comput. Surv. 46(4), 43:1–43:33 (2014)
Sanchez, D., Tettamanzi, A.G.B.: Generalizing quantification in fuzzy description logics. In: Reusch, B. (ed.) Proceedings 8th Fuzzy Days in Dortmund. Springer, Heidelberg (2004)
Sánchez, D., Tettamanzi, A.G.B.: Reasoning and quantification in fuzzy description logics. In: Bloch, I., Petrosino, A., Tettamanzi, A.G.B. (eds.) WILF 2005. LNCS (LNAI), vol. 3849, pp. 81–88. Springer, Heidelberg (2006)
Sanchez, D., Tettamanzi, A.G.B.: Fuzzy quantification in fuzzy description logics. In: Sanchez, E. (ed.) Capturing Intelligence: Fuzzy Logic and the Semantic Web. Elsevier, New York (2006)
Sanchez, E. (ed.): Fuzzy Logic and the Semantic Web. Capturing Intelligence, vol. 1. Elsevier Science, New York (2006)
Slavíček, V.: An ontology-driven fuzzy workflow system. In: van Emde Boas, P., Groen, F.C.A., Italiano, G.F., Nawrocki, J., Sack, H. (eds.) SOFSEM 2013. LNCS, vol. 7741, pp. 515–527. Springer, heidelberg (2013)
Stoilos, G., Stamou, G., Pan, J.Z.: Fuzzy extensions of OWL: logical properties and reduction to fuzzy description logics. Int. J. Approx. Reason. 51(6), 656–679 (2010)
Stoilos, G., Stamou, G.: Extending fuzzy description logics for the semantic web. In: 3rd International Workshop of OWL: Experiences and Directions (2007)
Stoilos, G., Stamou, G., Pan, J., Tzouvaras, V., Horrocks, I.: The fuzzy description logic f-SHIN. In: International Workshop on Uncertainty Reasoning for the Semantic Web (2005)
Stoilos, G., Simou, N., Stamou, G., Kollias, S.: Uncertainty and the semantic web. IEEE Intel. Syst. 21(5), 84–87 (2006)
Stoilos, G., Stamou, G., Tzouvaras, V., Pan, J.Z., Horrock, I.: A fuzzy description logic for multimedia knowledge representation. In: Proceedings of the International Workshop on Multimedia and the Semantic Web (2005)
Stoilos, G., Stamou, G.B., Pan, J.Z., Tzouvaras, V., Horrocks, I.: Reasoning with very expressive fuzzy description logics. J. Artif. Intel. Res. 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 Eureopean Conference on Artificial Intelligence (ECAI-06), pp. 457–461. IOS Press (2006)
Straccia, U.: A fuzzy description logic. In: Proceedings of the 15th National Conference on Artificial Intelligence (AAAI-98), Madison, USA, pp. 594–599 (1998)
Straccia, U.; Foundations of a logic based approach to multimedia document retrieval. Ph.D. thesis, Department of Computer Science, University of Dortmund, Dortmund, Germany, June 1999
Straccia, U.: A framework for the retrieval of multimedia objects based on four-valued fuzzy description logics. In: Crestani, F., Pasi, G. (eds.) Soft Computing in Information Retrieval: Techniques and Applications, pp. 332–357. Physica Verlag (Springer Verlag), Heidelberg (2000)
Straccia, U.: Reasoning within fuzzy description logics. J. Artif. Intel. Res. 14, 137–166 (2001)
Straccia, U.: Transforming fuzzy description logics into classical description logics. In: Alferes, J.J., Leite, J. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 385–399. Springer, Heidelberg (2004)
Straccia, U.: Uncertainty in description logics: a lattice-based approach. In: Proceedings of the 10th International Conference on Information Processing and Managment of Uncertainty in Knowledge-Based Systems (IPMU-04), pp. 251–258 (2004)
Straccia, U.: Description logics with fuzzy concrete domains. In: Bachus, F., Jaakkola, T. (eds.) 21st Conference on Uncertainty in Artificial Intelligence (UAI-05), pp. 559–567. AUAI Press, Edinburgh (2005)
Straccia, U.: Fuzzy ALC with fuzzy concrete domains. In: Proceeedings of the International Workshop on Description Logics (DL-05), pp. 96–103. CEUR, break Edinburgh (2005)
Straccia, U.: Answering vague queries in fuzzy DL-Lite. In: Proceedings of the 11th International Conference on Information Processing and Managment of Uncertainty in Knowledge-Based Systems, IPMU-06, pp. 2238–2245. E.D.K, Paris (2006)
Straccia, U.: Description logics over lattices. Int. J. Uncertainty, Fuzziness Knowl.-Based Syst. 14(1), 1–16 (2006)
Straccia, U.: Fuzzy description logic programs. In: Proceedings of the 11th International Conference on Information Processing and Managment of Uncertainty in Knowledge-Based Systems, IPMU-06, pp. 1818–1825. E.D.K, Paris (2006)
Straccia, U.: Towards Top-k query answering in description logics: the case of DL-Lite. In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds.) JELIA 2006. LNCS (LNAI), vol. 4160, pp. 439–451. Springer, Heidelberg (2006)
Straccia, U.: Uncertainty and description logic programs over lattices. In: Sanche, E. (ed.) Fuzzy Logic and the Semantic Web, Capturing Intelligence, Chap. 7, pp. 115–133. Elsevier, Amsterdam (2006)
Straccia, U.: Reasoning in Ł-\({\cal SHIF}\): an expressive fuzzy description logic under łukasiewicz semantics. Technical report TR-2007-10-18, Istituto di Scienza e Tecnologie dell’Informazione, Consiglio Nazionale delle Ricerche, Pisa, Italy (2007)
Straccia, U.: Fuzzy description logic programs. In: Marsala, C., Bouchon-Meunier, B., Yager, R.R., Rifqi, M. (eds.) Uncertainty and Intelligent Information Systems, Chap. 29, pp. 405–418. World Scientific, Singapore (2008)
Straccia, U.: Managing uncertainty and vagueness in description logics, logic programs and description logic programs. In: Baroglio, C., Bonatti, P.A., Małuszyński, J., Marchiori, M., Polleres, A., Schaffert, S. (eds.) Reasoning Web. LNCS, vol. 5224, pp. 54–103. Springer, Heidelberg (2008)
Straccia, U.: Multi criteria decision making in fuzzy description logics: a first step. In: Velásquez, J.D., Ríos, S.A., Howlett, R.J., Jain, L.C. (eds.) KES 2009, Part I. LNCS, vol. 5711, pp. 78–86. Springer, Heidelberg (2009)
Straccia, U.: Towards spatial reasoning in fuzzy description logics. In: 2009 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE-09), pp. 512–517. IEEE Computer Society (2009)
Straccia, U.: An ontology mediated multimedia information retrieval system. In: Proceedings of the the 40th International Symposium on Multiple-Valued Logic (ISMVL-10), pp. 319–324. IEEE Computer Society (2010)
Straccia, U.: Softfacts: a Top-k retrieval engine for ontology mediated access to relational databases. In: Proceedings of the 2010 IEEE International Conference on Systems, Man and Cybernetics (SMC-10), pp. 4115–4122. IEEE Press (2010)
Straccia, U.: Foundations of Fuzzy Logic and Semantic Web Languages. CRC Studies in Informatics Series. Chapman & Hall, Boca Raton (2013)
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-07), University of Ostrava, Ostrava, Czech Republic, vol. 2, pp. 213–220 (2007)
Straccia, U., Bobillo, F.: Mixed integer programming, general concept inclusions and fuzzy description logics. Mathw. Soft Comput. 14(3), 247–259 (2007)
Straccia, U., Mucci, M.: pFOIL-DL: learning (fuzzy) \({\cal EL}\) concept descriptions from crisp owl data using a probabilistic ensemble estimation. In: Proceedings of the 30th Annual ACM Symposium on Applied Computing (SAC-15), pp. 345–352. ACM, Salamanca (2015)
Straccia, U., Tinelli, E., Colucci, S., Di Noia, T., Di Sciascio, E.: Semantic-based Top-k retrieval for competence management. In: Rauch, J., Raś, Z.W., Berka, P., Elomaa, T. (eds.) ISMIS 2009. LNCS, vol. 5722, pp. 473–482. Springer, Heidelberg (2009)
Straccia, U., Tinelli, E., Di Noia, T., Di Sciascio, E., Colucci, S.: Top-k retrieval for automated human resource management. In: Proceedings of the 17th Italian Symposium on Advanced Database Systems (SEBD-09), pp. 161–168 (2009)
Straccia, U., Visco, G.: DL-Media: an ontology mediated multimedia information retrieval system. In: Proceeedings of the International Workshop on Description Logics (DL-07), vol. 250. CEUR, Insbruck (2007)
Straccia, U., Visco, G.: DLMedia: an ontology mediated multimedia information retrieval system. In: Proceedings of the Fourth International Workshop on Uncertainty Reasoning for the Semantic Web (URSW-08), Karlsruhe, Germany, 26 October 2008. CEUR Workshop Proceedings, vol. 423. CEUR-WS.org (2008)
Todorov, K., Hudelot, C., Popescu, A., Geibel, P.: Fuzzy ontology alignment using background knowledge. Int. J. Uncertainty, Fuzziness Knowl.-Based Syst. 22(1), 75–112 (2014)
Tresp, C., Molitor, R.: A description logic for vague knowledge. In: Proceedings of the 13th European Conference on Artificial Intelligence (ECAI-98), Brighton (England), August 1998
Venetis, T., Stoilos, G., Stamou, G., Kollias, S.: f-DLPs: extending description logic programs with fuzzy sets and fuzzy logic. In: IEEE International Conference on Fuzzy Systems (Fuzz-IEEE 2007) (2007)
Wallace, M.: Ontologies and soft computing in flexible querying. Control Cybern. 38(2), 481–507 (2009)
Wang, H., Ma, Z.M., Yin, J.: FRESG: a kind of fuzzy description logic reasoner. In: Bhowmick, S.S., Küng, J., Wagner, R. (eds.) DEXA 2009. LNCS, vol. 5690, pp. 443–450. Springer, Heidelberg (2009)
Yaguinuma, C.A., Santos, M.T.P., Camargo, H.A., Reformat, M.: A FML-based hybrid reasoner combining fuzzy ontology and mamdani inference. In: Proceedings of the 22nd IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2013) (2013)
Lu, J., Li, Y., Xu, B., Kang, D.: Discrete tableau algorithms for \({\cal SHI}\). In: Proceeedings of the International Workshop on Description Logics (DL-06). CEUR (2006)
Yen, J.: Generalizing term subsumption languages to fuzzy logic. In: Proceedings of the 12th International Joint Conference on Artificial Intelligence (IJCAI-91), Sydney, Australia, pp. 472–477 (1991)
Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)
Zhang, L., Yu, Y., Zhou, J., Lin, C., Yang, Y.: An enhanced model for searching in semantic portals. In: WWW 2005: Proceedings of the 14th International Conference on World Wide Web, pp. 453–462. ACM Press, New York (2005)
Zhou, Z., Qi, G., Liu, C., Hitzler, P., Mutharaju, R.: Reasoning with fuzzy-\({\cal EL}^{+}\) ontologies using mapreduce. In: 20th European Conference on Artificial Intelligence (ECAI-12), pp. 933–934. IOS Press (2012)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Straccia, U. (2015). All About Fuzzy Description Logics and Applications. In: Faber, W., Paschke, A. (eds) Reasoning Web. Web Logic Rules. Reasoning Web 2015. Lecture Notes in Computer Science(), vol 9203. Springer, Cham. https://doi.org/10.1007/978-3-319-21768-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-21768-0_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-21767-3
Online ISBN: 978-3-319-21768-0
eBook Packages: Computer ScienceComputer Science (R0)