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Reasoning and Explanation in \(\mathcal{EL}\) and in Expressive Description Logics

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Reasoning Web. Semantic Technologies for Software Engineering (Reasoning Web 2010)

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Abstract

Description Logics (DLs) are the formalism underlying the standard web ontology language OWL 2. DLs have formal semantics which are the basis for powerful reasoning services. In this paper, we introduce the basic notions of DLs and the techniques that realize subsumption—the fundamental reasoning service of DL systems. We discuss two reasoning methods for this service: the tableau method for expressive DLs such as \(\mathcal{ALC}\) and the completion method for the light-weight DL \(\mathcal{EL}\). We also present methods for generating explanations for computed subsumption relationships in these two DLs.

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References

  1. Baader, F.: Description logic terminology. In: [6], pp. 485–495. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  2. Baader, F.: Description logics. In: Tessaris, S., Franconi, E., Eiter, T., Gutierrez, C., Handschuh, S., Rousset, M.-C., Schmidt, R.A. (eds.) Reasoning Web. Semantic Technologies for Information Systems. LNCS, vol. 5689, pp. 1–39. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  3. Baader, F., Bauer, A., Baumgartner, P., Cregan, A., Gabaldon, A., Ji, K., Lee, K., Rajaratnam, D., Schwitter, R.: A novel architecture for situation awareness systems. In: Giese, M., Waaler, A. (eds.) TABLEAUX 2009. LNCS, vol. 5607, pp. 77–92. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  4. Baader, F., Brandt, S., Lutz, C.: Pushing the \(\mathcal{EL}\) envelope. In: Proc. of the 19th Int. Joint Conf. on Artificial Intelligence (IJCAI-05), Edinburgh, UK. Morgan-Kaufmann Publishers, San Francisco (2005)

    Google Scholar 

  5. Baader, F., Brandt, S., Lutz, C.: Pushing the \(\mathcal{EL}\) envelope further. In: Clark, K., Patel-Schneider, P.F. (eds.) Proc. of the OWLED Workshop (2008)

    Google Scholar 

  6. Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  7. Baader, F., Franconi, E., Hollunder, B., Nebel, B., Profitlich, H.-J.: An empirical analysis of optimization techniques for terminological representation systems or: Making KRIS get a move on. Applied Artificial Intelligence. Special Issue on Knowledge Base Management 4, 109–132 (1994)

    Google Scholar 

  8. Baader, F., Hollunder, B.: Embedding defaults into terminological knowledge representation formalisms. In: Proc. of the 3rd Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR-92), pp. 306–317. Morgan Kaufmann, Los Altos (1992)

    Google Scholar 

  9. Baader, F., Knechtel, M., Peñaloza, R.: A generic approach for large-scale ontological reasoning in the presence of access restrictions to the ontology’s axioms. In: Bernstein, A., Karger, D.R., Heath, T., Feigenbaum, L., Maynard, D., Motta, E., Thirunarayan, K. (eds.) ISWC 2009. LNCS, vol. 5823, pp. 49–64. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Baader, F., Küsters, R., Molitor, R.: Computing least common subsumer in description logics with existential restrictions. In: Dean, T. (ed.) Proc. of the 16th Int. Joint Conf. on Artificial Intelligence (IJCAI-99), pp. 96–101. Morgan Kaufmann, Los Altos (1999)

    Google Scholar 

  11. Baader, F., Lutz, C., Suntisrivaraporn, B.: CEL—a polynomial-time reasoner for life science ontologies. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 287–291. Springer, Heidelberg (2006), http://lat.inf.tu-dresden.de/systems/cel/

    Chapter  Google Scholar 

  12. Baader, F., Lutz, C., Suntisrivaraporn, B.: Is tractable reasoning in extensions of the description logic \(\mathcal{EL}\) useful in practice? Journal of Logic, Language and Information, Special Issue on Method for Modality, M4M (2007)

    Google Scholar 

  13. Baader, F., Lutz, C., Turhan, A.-Y.: Small is again beautiful in description logics. KI – Künstliche Intelligenz 24(1), 25–33 (2010)

    Article  Google Scholar 

  14. Baader, F., Peñaloza, R.: Axiom pinpointing in general tableaux. Journal of Logic and Computation; Special Issue: Tableaux and Analytic Proof Methods 20(1), 5–34 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  15. Baader, F., Peñaloza, R., Suntisrivaraporn, B.: Pinpointing in the description logic \(\mathcal{EL}\). In: Calvanese, D., Franconi, E., Haarslev, V., Lembo, D., Motik, B., Tessaris, S., Turhan, A.-Y. (eds.) Proc. of the 2007 Description Logic Workshop (DL 2007), CEUR-WS (2007)

    Google Scholar 

  16. Baader, F., Peñaloza, R., Suntisrivaraporn, B.: Pinpointing in the description logic \({{\mathcal{EL}}^+}\). In: Hertzberg, J., Beetz, M., Englert, R. (eds.) KI 2007. LNCS (LNAI), vol. 4667, pp. 52–67. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  17. Baader, F., Sattler, U.: An overview of tableau algorithms for description logics. Studia Logica 69, 5–40 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Baader, F., Sertkaya, B., Turhan, A.-Y.: Computing the least common subsumer w.r.t. a background terminology. Journal of Applied Logics (2007)

    Google Scholar 

  19. Baader, F., Suntisrivaraporn, B.: Debugging SNOMED CT using axiom pinpointing in the description logic \(\mathcal{EL}^+\). In: Proc. of the International Conference on Representing and Sharing Knowledge Using SNOMED (KR-MED’08), Phoenix, Arizona (2008)

    Google Scholar 

  20. Bailey, J., Stuckey, P.J.: Discovery of minimal unsatisfiable subsets of constraints using hitting set dualization. In: Hermenegildo, M.V., Cabeza, D. (eds.) PADL 2004. LNCS, vol. 3350, pp. 174–186. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  21. Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  22. Borgida, A., Patel-Schneider, P.F.: A semantics and complete algorithm for subsumption in the CLASSIC description logic. Journal of Artificial Intelligence Research 1, 277–308 (1994)

    MATH  Google Scholar 

  23. Brachman, R.J., Borgida, A., McGuinness, D.L., Alperin Resnick, L.: The CLASSIC knowledge representation system or KL-ONE: the next generation. Preprints of the Workshop on Formal Aspects of Semantic Networks, Two Harbors, Cal. (1989)

    Google Scholar 

  24. Brachman, R.J., Levesque, H.J.: Readings in Knowledge Representation. Morgan Kaufmann, Los Altos (1985)

    MATH  Google Scholar 

  25. Brandt, S.: Polynomial time reasoning in a description logic with existential restrictions, GCI axioms, and—what else? In: de Mantáras, R.L., Saitta, L. (eds.) Proc. of the 16th European Conf. on Artificial Intelligence (ECAI-04), pp. 298–302. IOS Press, Amsterdam (2004)

    Google Scholar 

  26. Brandt, S.: Reasoning in \(\mathcal{ELH}\) w.r.t. general concept inclusion axioms. LTCS-Report LTCS-04-03, Chair for Automata Theory, Institute for Theoretical Computer Science, Dresden University of Technology, Germany (2004), http://lat.inf.tu-dresden.de/research/reports.html

  27. Brandt, S., KĂĽsters, R., Turhan, A.-Y.: Approximation and difference in description logics. In: Fensel, D., McGuinness, D., Williams, M.-A. (eds.) Proc. of the 8th Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR-02). Morgan Kaufmann Publishers, San Francisco (2002)

    Google Scholar 

  28. Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: DL-Lite: Tractable description logics for ontologies. In: Veloso, M.M., Kambhampati, S. (eds.) Proc. of the 20th Nat. Conf. on Artificial Intelligence (AAAI’05), pp. 602–607. AAAI Press/The MIT Press (2005)

    Google Scholar 

  29. Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Data complexity of query answering in description logics. In: Proc. of the 10th Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR 2006), pp. 260–270 (2006)

    Google Scholar 

  30. Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Tractable reasoning and efficient query answering in description logics: The DL-Lite family. Journal of Automated Reasoning 39(3), 385–429 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  31. Calvanese, D., Giacomo, G.D.: Expressive description logics. In: [6], pp. 178–218. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  32. Cuenca Grau, B., Horrocks, I., Kazakov, Y., Sattler, U.: Modular reuse of ontologies: Theory and practice. Journal of Artificial Intelligence Research 31, 273–318 (2008)

    MathSciNet  MATH  Google Scholar 

  33. Cuenca Grau, B., Kazakov, Y., Horrocks, I., Sattler, U.: A logical framework for modular integration of ontologies. In: Proc. of the 20th Int. Joint Conf. on Artificial Intelligence (IJCAI-07), pp. 298–303 (2007)

    Google Scholar 

  34. Davydov, G., Davydova, I., Büning, H.K.: An efficient algorithm for the minimal unsatisfiability problem for a subclass of cnf. Ann. Math. Artif. Intell. 23(3-4), 229–245 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  35. Donini, F.M., Colucci, S., Di Noia, T., Di Sciascio, E.: A tableaux-based method for computing least common subsumers for expressive description logics. In: Proc. of the Twenty-First International Joint Conference on Artificial Intelligence (IJCAI-09), pp. 739–745. AAAI, Menlo Park (July 2009)

    Google Scholar 

  36. Eiter, T., Lutz, C., Ortiz, M., Simkus, M.: Query answering in description logics with transitive roles. In: Proc. of the 21st International Joint Conference on Artificial Intelligence IJCAI’09. AAAI Press, Menlo Park (2009)

    Google Scholar 

  37. Fitting, M.: Basic modal logic. In: Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 1, pp. 365–448. Oxford Science Publications, Oxford (1993)

    Google Scholar 

  38. Ghilardi, S., Lutz, C., Wolter, F.: Did I damage my ontology? a case for conservative extensions in description logics. In: Doherty, P., Mylopoulos, J., Welty, C. (eds.) Proc. of the 10th Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR-06), pp. 187–197. AAAI Press, Menlo Park (2006)

    Google Scholar 

  39. Glimm, B., Horrocks, I., Lutz, C., Sattler, U.: Conjunctive query answering for the description logic \({\mathcal{SHIQ}}\). In: Veloso, M.M. (ed.) Proc. of the 20th Int. Joint Conf. on Artificial Intelligence (IJCAI-07), pp. 399–404 (2007)

    Google Scholar 

  40. Grädel, E.: On the restraining power of guards. Journal of Symbolic Logic 64, 1719–1742 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  41. Grädel, E., Kolaitis, P.G., Vardi, M.Y.: On the decision problem for two-variable first-order logic. Bulletin of Symbolic Logic 3(1), 53–69 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  42. Haarslev, V., Möller, R.: High performance reasoning with very large knowledge bases: A practical case study. In: Nebel, B. (ed.) Proc. of the 17th Int. Joint Conf. on Artificial Intelligence (IJCAI-01), pp. 161–166 (2001)

    Google Scholar 

  43. Haarslev, V., Möller, R.: RACER system description. In: Goré, R., Leitsch, A., Nipkov, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, p. 701. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  44. Haarslev, V., Möller, R.: Optimization techniques for retrieving resources described in OWL/RDF documents: First results. In: Proc. of the 9th Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR-04), pp. 163–173 (2004)

    Google Scholar 

  45. Haarslev, V., Möller, R., Turhan, A.-Y.: Exploiting pseudo models for TBox and ABox reasoning in expressive description logics. In: Goré, R., Leitsch, A., Nipkov, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, p. 61. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  46. Hofmann, M.: Proof-theoretic approach to description-logic. In: Panangaden, P. (ed.) Proc. of the 20th Ann. IEEE Symp. on Logic in Computer Science (LICS-05), pp. 229–237. IEEE Computer Society Press, Los Alamitos (2005)

    Chapter  Google Scholar 

  47. Horridge, M., Parsia, B., Sattler, U.: Laconic and precise justifications in OWL. In: ISWC’08 The International Semantic Web Conference 2008, Karlsruhe, Germany (2008)

    Google Scholar 

  48. Horrocks, I.: Optimising Tableaux Decision Procedures for Description Logics. PhD thesis, University of Manchester (1997)

    Google Scholar 

  49. Horrocks, I.: Using an expressive description logic: FaCT or fiction? In: Cohn, A., Schubert, L., Shapiro, S. (eds.) Proc. of the 6th Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR-98), pp. 636–647 (1998)

    Google Scholar 

  50. Horrocks, I.: Reasoning with expressive description logics: Theory and practice. In: Voronkov, A. (ed.) CADE 2002. LNCS (LNAI), vol. 2392, pp. 1–15. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  51. Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible \(\mathcal{SROIQ}\). In: Doherty, P., Mylopoulos, J., Welty, C. (eds.) Proc. of the 10th Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR-06), pp. 57–67. AAAI Press, Menlo Park (2006)

    Google Scholar 

  52. Horrocks, I., Patel-Schneider, P.: Optimizing description logic subsumption. Journal of Logic and Computation 9(3), 267–293 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  53. Horrocks, I., Patel-Schneider, P., van Harmelen, F.: From \(\mathcal{SHIQ}\) and RDF to OWL: The making of a web ontology language. Journal of Web Semantics 1(1), 7–26 (2003)

    Article  Google Scholar 

  54. Horrocks, I., Sattler, U.: A description logic with transitive and inverse roles and role hierarchies. Journal of Logic and Computation 9(3), 385–410 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  55. Horrocks, I., Sattler, U.: Optimised reasoning for \(\mathcal {SHIQ}\). In: Proc. of the 15th European Conference on Artificial Intelligence (2002)

    Google Scholar 

  56. Horrocks, I., Sattler, U.: A tableaux decision procedure for \(\cal{SHOIQ}\). In: Proc. of the 19th Int. Joint Conf. on Artificial Intelligence (IJCAI-05). Morgan Kaufmann, San Francisco (January 2005)

    Google Scholar 

  57. Horrocks, I., Sattler, U.: A tableau decision procedure for \(\mathcal{SHOIQ}\). J. of Automated Reasoning 39(3), 249–276 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  58. Horrocks, I., Sattler, U., Tobies, S.: Practical reasoning for very expressive description logics. J. of the Interest Group in Pure and Applied Logic 8(3), 239–264 (2000)

    MathSciNet  MATH  Google Scholar 

  59. Hustadt, U., Schmidt, R.A., Georgieva, L.: A survey of decidable first-order fragments and description logics. Journal of Relational Methods in Computer Science 1, 251–276 (2004)

    Google Scholar 

  60. Kalyanpur, A., Parsia, B., Horridge, M., Sirin, E.: Finding all justifications of owl dl entailments. In: Aberer, K., Choi, K.-S., Noy, N., Allemang, D., Lee, K.-I., Nixon, L.J.B., Golbeck, J., Mika, P., Maynard, D., Mizoguchi, R., Schreiber, G., Cudré-Mauroux, P. (eds.) ASWC 2007 and ISWC 2007. LNCS, vol. 4825, pp. 267–280. Springer, Heidelberg (2007)

    Google Scholar 

  61. Kalyanpur, A., Parsia, B., Sirin, E., Cuenca Grau, B.: Repairing unsatisfiable concepts in owl ontologies. In: Sure, Y., Domingue, J. (eds.) ESWC 2006. LNCS, vol. 4011, pp. 170–184. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  62. Kalyanpur, A., Parsia, B., Sirin, E., Cuenca Grau, B., Hendler, J.: Swoop: A web ontology editing browser. J. Web Sem. 4(2), 144–153 (2006)

    Article  Google Scholar 

  63. Kalyanpur, A., Parsia, B., Sirin, E., Hendler, J.A.: Debugging unsatisfiable classes in OWL ontologies. J. Web Sem. 3(4), 268–293 (2005)

    Article  Google Scholar 

  64. Kazakov, Y.: \(\mathcal{RIQ}\) and \(\mathcal{SROIQ}\) are harder than \(\mathcal{SHOIQ}\). In: Brewka, G., Lang, J. (eds.) Proc. of the 11th Int. Conf. on the Principles of Knowledge Representation and Reasoning (KR-08), pp. 274–284. AAAI Press, Menlo Park (2008)

    Google Scholar 

  65. Liffiton, M.H., Sakallah, K.A.: Algorithms for computing minimal unsatisfiable subsets of constraints. J. Autom. Reasoning 40(1), 1–33 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  66. Lutz, C.: In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) LPAR 1999. LNCS, vol. 1705, Springer, Heidelberg (1999)

    Google Scholar 

  67. Lutz, C.: The complexity of conjunctive query answering in expressive description logics. In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 179–193. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  68. Lutz, C., Sattler, U., Wolter, F.: Description logics and the two-variable fragment. In: McGuiness, D., Pater-Schneider, P., Goble, C., Möller, R. (eds.) Proc. of the 2001 International Workshop in Description Logics (DL-2001), Stanford, California, USA, pp. 66–75 (2001)

    Google Scholar 

  69. Lutz, C., Walther, D., Wolter, F.: Conservative extensions in expressive description logics. In: Proc. of the 20th Int. Joint Conf. on Artificial Intelligence (IJCAI-07). AAAI Press, Menlo Park (2007)

    Google Scholar 

  70. Lutz, C., Wolter, F.: Deciding inseparability and conservative extensions in the description logic \(\mathcal{EL}\). Journal of Symbolic Computation 45(2), 194–228 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  71. Mendez, J., Suntisrivaraporn, B.: Reintroducing cel as an owl 2 el reasoner. In: Cuenca Grau, B., Horrocks, I., Motik, B., Sattler, U. (eds.) Proc. of the 2008 Description Logic Workshop (DL 2009), vol. 477. CEUR-WS (2009)

    Google Scholar 

  72. Meyer, T., Lee, K., Booth, R., Pan, J.Z.: Finding maximally satisfiable terminologies for the description logic \(\mathcal{{ALC}}\). In: Proc. of the 21st Nat. Conf. on Artificial Intelligence (AAAI’06), AAAI Press/The MIT Press (2006)

    Google Scholar 

  73. Minsky, M.: A framework for representing knowledge. Technical report, MIT-AI Laboratory, Cambridge, MA, USA (1974)

    Google Scholar 

  74. Motik, B.: Reasoning in Description Logics using Resolution and Deductive Databases. PhD thesis, Universität Karlsruhe (2006)

    Google Scholar 

  75. Motik, B., Cuenca Grau, B., Horrocks, I., Wu, Z., Fokoue, A., Lutz, C.: Owl 2 web ontology language profiles. W3C Recommendation (October 27, 2009), http://www.w3.org/TR/2009/REC-owl2-profiles-20091027/

  76. Motik, B., Sattler, U.: A Comparison of Techniques for Querying Large Description Logic ABoxes. In: Hermann, M., Voronkov, A. (eds.) LPAR 2006. LNCS (LNAI), vol. 4246, pp. 227–241. Springer, Heidelberg (2006), http://kaon2.semanticweb.org/

    Chapter  Google Scholar 

  77. Motik, B., Shearer, R., Horrocks, I.: A hypertableau calculus for \(\cal{SHIQ}\). In: Calvanese, D., Franconi, E., Haarslev, V., Lembo, D., Motik, B., Tessaris, S., Turhan, A.-Y. (eds.) Proc. of the 2007 Description Logic Workshop, DL 2007 (2007)

    Google Scholar 

  78. Motik, B., Shearer, R., Horrocks, I.: Optimized Reasoning in Description Logics using Hypertableaux. In: Pfennig, F. (ed.) Proc. of the 23th Conf. on Automated Deduction (CADE-23). LNCS (LNAI), pp. 67–83. Springer, Heidelberg (2007)

    Google Scholar 

  79. Nebel, B.: Computational complexity of terminological reasoning in BACK. Artificial Intelligence Journal 34(3), 371–383 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  80. Nebel, B.: Terminological reasoning is inherently intractable. Artificial Intelligence Journal 43, 235–249 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  81. Nebel, B., von Luck, K.: Hybrid reasoning in BACK. In: Proc. of the 3rd Int. Sym. on Methodologies for Intelligent Systems (ISMIS-88), pp. 260–269. North-Holland Publ. Co., Amsterdam (1988)

    Google Scholar 

  82. Ortiz, M., Calvanese, D., Eiter, T.: Data complexity of query answering in expressive description logics via tableaux. Journal of Automated Reasoning 41(1), 61–98 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  83. Parsia, B., Sirin, E., Kalyanpur, A.: Debugging OWL Ontologies. In: Ellis, A., Hagino, T. (eds.) Proc. of the 14th Int. World Wide Web Conference (WWW 2005), Japan, pp. 633–640 (2005)

    Google Scholar 

  84. Patel-Schneider, P., McGuinness, D.L., Brachman, R.J., Resnick, L.A., Borgida, A.: The CLASSIC knowledge representation system: Guiding principles and implementation rational. SIGART Bulletin 2(3), 108–113 (1991)

    Article  Google Scholar 

  85. Quillian, M.R.: Word concepts: A theory and simulation of some basic capabilities. Behavioral Science 12, 410–430 (1967) Republished in [24]

    Article  Google Scholar 

  86. Racer Systems GmbH & Co. KG. RacerPro Reference Manual Version 1.9 (December 2005), http://www.racer-systems.com/products/racerpro/reference-manual-1-9.pdf

  87. Rector, A., Horrocks, I.: Experience building a large, re-usable medical ontology using a description logic with transitivity and concept inclusions. In: Proc. of the Workshop on Ontological Engineering. AAAI Spring Symposium, AAAI’97 (1997)

    Google Scholar 

  88. Sattler, U., Calvanese, D., Molitor, R.: Relationships with other formalisms. In: [6], pp. 137–177. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  89. Schild, K.: A correspondence theory for terminological logics: preliminary report. In: Mylopoulos, J., Reiter, R. (eds.) Proc. of the 12th Int. Joint Conf. on Artificial Intelligence (IJCAI-91), Sydney, Australia (1991)

    Google Scholar 

  90. Schlobach, S., Cornet, R.: Non-standard reasoning services for the debugging of description logic terminologies. In: Gottlob, G., Walsh, T. (eds.) Proc. of the 18th Int. Joint Conf. on Artificial Intelligence (IJCAI-03), Mexico, pp. 355–362. Morgan Kaufmann, Los Altos (2003)

    Google Scholar 

  91. Schmidt-SchauĂź, M., Smolka, G.: Attributive concept descriptions with unions and complements. Technical Report SR-88-21, Deutsches Forschungszentrum fĂĽr KĂĽnstliche Intelligenz (DFKI), Kaiserslautern, Germany (1988)

    Google Scholar 

  92. Schmidt-Schauß, M., Smolka, G.: Attributive concept descriptions with complements. Artificial Intelligence Journal 48(1), 1–26 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  93. Sirin, E., Parsia, B.: Pellet system description. In: Parsia, B., Sattler, U., Toman, D. (eds.) Description Logics, CEUR Workshop Proceedings, vol. 189. CEUR-WS.org (2006)

    Google Scholar 

  94. Sowa, J.F. (ed.): Principles of Semantic Networks. Morgan Kaufmann, Los Altos (1991)

    MATH  Google Scholar 

  95. Sowa, J.F.: Semantic Networks. In: Encyclopedia of Artificial Intelligence. John Wiley & Sons, New York (1992)

    Google Scholar 

  96. Springer, T., Turhan, A.-Y.: Employing description logics in ambient intelligence for modeling and reasoning about complex situations. Journal of Ambient Intelligence and Smart Environments 1(3), 235–259 (2009)

    Google Scholar 

  97. Suntisrivaraporn, B.: Polynomial-Time Reasoning Support for Design and Maintenance of Large-Scale Biomedical Ontologies. PhD thesis, Fakultät Informatik, TU Dresden (2009), http://lat.inf.tu-dresden.de/research/phd/#Sun-PhD-2008

  98. Tobies, S.: The complexity of reasoning with cardinality restrictions and nominals in expressive description logics. Journal of Artificial Intelligence Research 12, 199–217 (2000)

    MathSciNet  MATH  Google Scholar 

  99. Tsarkov, D., Horrocks, I.: FaCT++ description logic reasoner: System description. In: Proc. of the 3rd Int. Joint Conf. on Automated Reasoning, IJCAR-06 (2006), FaCT++ download page, http://owl.man.ac.uk/factplusplus/

  100. Tsarkov, D., Horrocks, I., Patel-Schneider, P.F.: Optimising terminological reasoning for expressive description logics. Journal of Automated Reasoning (2007)

    Google Scholar 

  101. Turhan, A.-Y.: On the Computation of Common Subsumers in Description Logics. PhD thesis, TU Dresden, Institute for Theoretical Computer Science (2007)

    Google Scholar 

  102. W3C OWL Working Group. Owl 2 web ontology language document overview. W3C Recommendation (October 27, 2009), http://www.w3.org/TR/2009/REC-owl2-overview-20091027/

  103. Zhang, L., Malik, S.: Validating sat solvers using an independent resolution-based checker: Practical implementations and other applications. In: Design, Automation and Test in Europe Conference and Exposition (DATE 2003), Munich, Germany, March 3-7, pp. 10880–10885. IEEE Computer Society, Los Alamitos (2003)

    Google Scholar 

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Turhan, AY. (2010). Reasoning and Explanation in \(\mathcal{EL}\) and in Expressive Description Logics. In: AĂźmann, U., Bartho, A., Wende, C. (eds) Reasoning Web. Semantic Technologies for Software Engineering. Reasoning Web 2010. Lecture Notes in Computer Science, vol 6325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15543-7_1

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