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Reasoning in Description Logics: Basics, Extensions, and Relatives

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Reasoning Web (Reasoning Web 2007)

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Abstract

This tutorial covers the very basics of Description Logics (DLs): first, we present the primary DL , namely its syntax, semantics, and reasoning problems, making use of a running example. Next, we discuss a few important extensions and explain DL’s relationship with first order logic, with modal logic, with OWL, and with rule-based formalisms, and give a brief sketch of tableau-based reasoning algorithms for DLs.

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References

  1. Andréka, H., van Benthem, J., Németi, I.: Modal languages and bounded fragments of predicate logic. Journal of Philosophical Logic 27(3), 217–274 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  2. Areces, C.: Logic Engineering. The Case of Description and Hybrid Logics. PhD thesis, ILLC, University of Amsterdam (2000)

    Google Scholar 

  3. Areces, C., Blackburn, P., Marx, M.: A road-map on complexity for hybrid logics. In: Flum, J., Rodríguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 307–321. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  4. Artale, A., Franconi, E.: A survey of temporal extensions of description logics. Annals of Mathematics and Artificial Intelligence 30(1-4), 171–210 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Baader, F.: A formal definition for the expressive power of terminological knowledge representation languages. Journal of Logic and Computation 6(1), 33–54 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  6. Baader, F., Brandt, S., Küsters, R.: Matching under side conditions in description logics. In: Nebel, B. (ed.) IJCAI-01. Proc. of the 17th Int. Joint Conf. on Artificial Intelligence, Seattle, Washington, pp. 213–218. Morgan Kaufmann, Los Altos (2001)

    Google Scholar 

  7. 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)

    MATH  Google Scholar 

  8. Baader, F., Hanschke, P.: A schema for integrating concrete domains into concept languages. In: IJCAI-91. Proc. of the 12th Int. Joint Conf. on Artificial Intelligence, Sydney, pp. 452–457 (1991)

    Google Scholar 

  9. Baader, F., Sattler, U.: Expressive number restrictions in description logics. Journal of Logic and Computation 9(3), 319–350 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  10. Baader, F., Sattler, U.: An overview of tableau algorithms for description logics. Studia Logica 69, 5–40 (2001) An abridged version appeared in Tableaux 2000. LNCS(LNAI), vol. 1847, Springer, Heidelberg (2000)

    Google Scholar 

  11. Baader, F., Turhan, A.-Y.: On the problem of computing small representations of least common subsumers. In: Jarke, M., Koehler, J., Lakemeyer, G. (eds.) KI 2002. LNCS (LNAI), vol. 2479, Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  12. Baader, F., Hollunder, B.: How to prefer more specific defaults in terminological default logic. In: IJCAI-93. Proc. of the 13th Int. Joint Conf. on Artificial Intelligence, Chambery, France, pp. 669–674. Morgan Kaufmann, Los Altos (1993)

    Google Scholar 

  13. Bechhofer, S., Horrocks, I., Goble, C., Stevens, R.: OilEd: a reason-able ontology editor for the semantic web. In: DL 2001. Proc. of the 2001 Description Logic Workshop, pp. 1–9. CEUR (2001), http://ceur-ws.org/

  14. Berners-Lee, T., Hendler, J., Lassila, O.: The semantic Web. Scientific American 284(5), 34–43 (2001)

    Article  Google Scholar 

  15. Bodenreider, O., Stevens, R.: Bio-ontologies: current trends and future directions. Briefings in Bioinformatics 7(3), 256–274 (2006)

    Article  Google Scholar 

  16. Borgida, A.: On the relative expressive power of Description Logics and Predicate Calculus. Artificial Intelligence Journal 82(1) (1996)

    Google Scholar 

  17. Borst, P., Akkermans, H., Top, J.: Engineering ontologies. International Journal of Human-Computer Studies 46, 365–406 (1997)

    Article  Google Scholar 

  18. Brandt, S., Küsters, R., Turhan, A.-Y.: Approximation and difference in description logics. In: Fensel, D., Giunchiglia, F., McGuiness, D., Williams, M.-A. (eds.) KR-02. Proc. of the 8th Int. Conf. on the Principles of Knowledge Representation and Reasoning, pp. 203–214. Morgan Kaufmann, Los Altos (2002)

    Google Scholar 

  19. Calvanese, D., De Giacomo, G., Lembo, D., Lenzerini, M., Rosati, R.: Epistemic first-order queries over description logic knowledge bases. In: DL 2006. Proc. of the 2006 Description Logic Workshop. CEUR (2006)

    Google Scholar 

  20. Calvanese, D., De Giacomo, G., Lenzerini, M., Nardi, D.: Reasoning in expressive description logics. In: Robinson, A., Voronkov, A. (eds.) Handbook of Automated Reasoning, Elsevier Science Publishers (North-Holland), Amsterdam (2001)

    Google Scholar 

  21. Calvanese, D., Lenzerini, M., Nardi, D.: Description logics for conceptual data modeling. In: Chomicki, J., Saake, G. (eds.) Logics for Databases and Information Systems, pp. 229–263. Kluwer Academic Publishers, Dordrecht (1998)

    Google Scholar 

  22. Cuenca Grau, B., Horrocks, I., Kazakov, Y., Sattler, U.: Just the right amount: Extracting modules from ontologies. In: WWW 2007. Proc. of the Sixteenth International World Wide Web Conference (to appear)

    Google Scholar 

  23. De Giacomo, G.: Decidability of Class-Based Knowledge Representation Formalisms. PhD thesis, Università degli Studi di Roma “La Sapienza” (1995)

    Google Scholar 

  24. De Giacomo, G., Lenzerini, M.: Boosting the correspondence between description logics and propositional dynamic logics (extended abstract). In: AAAI-94. Proc. of the 12th Nat. Conf. on Artificial Intelligence, AAAI Press, Stanford, California, USA (1994)

    Google Scholar 

  25. Donini, F., Nardi, D., Rosati, R.: Description logics of minimal knowledge and negation as failure. ACM Trans. Comput. Log. 3(2), 177–225 (2002)

    Article  MathSciNet  Google Scholar 

  26. Donini, F.M., Lenzerini, M., Nardi, D., Schaerf, A.: AL-log: Integrating Datalog and Description Logics. J. of Intelligent Information Systems 10(3), 227–252 (1998)

    Article  Google Scholar 

  27. Eiter, T., Lukasiewicz, T., Schindlauer, R., Tompits, H.: Combining answer set programming with description logics for the semantic web. In: KR-04. Proc. of the 9th Int. Conf. on the Principles of Knowledge Representation and Reasoning, pp. 141–151 (2004)

    Google Scholar 

  28. Gelfond, M., Lifschitz, V.: The stable model semantics for logic programming. In: Kowalski, R., Bowen, K. (eds.) Proc. of the 5th Int. Conf. on Logic Programming, pp. 1070–1080. The MIT Press, Cambridge (1988)

    Google Scholar 

  29. Gonçalvès, E., Grädel, E.: Decidability issues for action guarded logics. In: DL 2000. Proc. of the 2000 Description Logic Workshop, pp. 123–132. CEUR (2000), http://ceur-ws.org/

  30. Grädel, E.: On the restraining power of guards. Journal of Symbolic Logic 64(4), 1719–1742 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  31. Grädel, E.: Why are modal logics so robustly decidable. In: Paun, G., Rozenberg, G., Salomaa, A. (eds.) Current Trends in Theoretical Computer Science. Entering the 21st Century, pp. 393–408. World Scientific, Singapore (2001)

    Google Scholar 

  32. Grädel, E., Kolaitis, P., Vardi, M.: On the Decision Problem for Two-Variable First-Order Logic. Bulletin of Symbolic Logic 3, 53–69 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  33. Cuenca Grau, B., Horrocks, I., Parsia, B., Patel-Schneider, P., Sattler, U.: Next steps for owl. In: Proc. of OWL: Experiences and Directions. CEUR (2006), http://ceur-ws.org/

  34. Gruber, T.R.: Towards Principles for the Design of Ontologies Used for Knowledge Sharing. In: Guarino, N., Poli, R. (eds.) Formal Ontology in Conceptual Analysis and Knowledge Representation, Deventer, The Netherlands, Kluwer Academic Publishers, Dordrecht (1993)

    Google Scholar 

  35. Haarslev, V., Möller, R.: Consistency testing: The RACE experience. In: Dyckhoff, R. (ed.) TABLEAUX 2000. LNCS, vol. 1847, pp. 1–18. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  36. Haarslev, V., Möller, R.: RACER system description. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, Springer, Heidelberg (2001)

    Google Scholar 

  37. Hladik, J.: Implementation and optimisation of a tableau algorithm for the guarded fragment. In: Egly, U., Fermüller, C. (eds.) TABLEAUX 2002. LNCS (LNAI), vol. 2381, Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  38. Horridge, M., Tsarkov, D.: Supporting early adoption of OWL 1.1 with Protege-OWL and FaCT++. In: Proc. of OWL: Experiences and Directions. CEUR (2006), http://ceur-ws.org/

  39. Horrocks, I.: Using an Expressive Description Logic: FaCT or Fiction? In: KR-98. Proc. of the 6th Int. Conf. on the Principles of Knowledge Representation and Reasoning, Morgan Kaufmann, Los Altos (1998)

    Google Scholar 

  40. Horrocks, I., Kutz, O., Sattler, U.: The even more irresistible \(\mathcal{SROIQ}\). In: KR-2006. Proc. of the 10th International Conference of Knowledge Representation and Reasoning, Morgan Kaufmann, Los Altos (2006)

    Google Scholar 

  41. Horrocks, I., Motik, B., Sattler, U.: Bridging the gap between owl and relational databases. In: Proc. of the Sixteenth International World Wide Web Conference (WWW 2007) (to appear)

    Google Scholar 

  42. Horrocks, I., Patel-Schneider, P.F.: A Proposal for an OWL Rules Language. In: WWW 2004. Proc. of the Thirteenth Int’l World Wide Web Conf., ACM, New York (2004)

    Google Scholar 

  43. Horrocks, I., Patel-Schneider, P.F., van Harmelen, F.: From SHIQ and RDF to OWL: The making of a web ontology language, vol. 1(1). John Wiley & Sons, Chichester (2003)

    Google Scholar 

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

    Google Scholar 

  45. Horrocks, I., Sattler, U.: Decidability of SHIQ with complex role inclusion axioms. In: IJCAI-03. Proc. of the 18th Int. Joint Conf. on Artificial Intelligence, Morgan Kaufmann, Los Altos (2003)

    Google Scholar 

  46. Horrocks, I., Sattler, U.: A tableau decision procedure for \(\mathcal{SHOIQ}\). Journal of Automated Reasoning (to appear)

    Google Scholar 

  47. Horrocks, I., Sattler, U., Tobies, S.: Practical reasoning for expressive description logics. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) LPAR 1999. LNCS, vol. 1705, pp. 161–180. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  48. Horrocks, I., Sattler, U., Tobies, S.: Practical reasoning for very expressive description logics. Logic Journal of the IGPL 8(3), 239–264 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  49. Horrocks, I., Patel-Schneider, P.F.: Optimising propositional modal satisfiability for description logic subsumption. In: Calmet, J., Plaza, J. (eds.) AISC 1998. LNCS (LNAI), vol. 1476, Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  50. Hustadt, U., Schmidt, R.A.: Issues of decidability for description logics in the framework of resolution. In: Caferra, R., Salzer, G. (eds.) Automated Deduction in Classical and Non-Classical Logics. LNCS (LNAI), vol. 1761, pp. 191–205. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  51. Kalyanpur, A., Parsia, B., Sirin, E., Cuenca-Grau, B., Hendler, J.: Swoop: A ’Web’ ontology editing browser, vol. 4(2). John Wiley & Sons, Chichester (2005)

    Google Scholar 

  52. Kalyanpur, A., Parsia, B., Sirin, E., Hendler, J.: Debugging unsatisfiable classes in owl ontologies, vol. 3(4). John Wiley & Sons, Chichester (2005)

    Google Scholar 

  53. Küsters, R.: Non-Standard Inferences in Description Logics. In: Küsters, R. (ed.) Non-Standard Inferences in Description Logics. LNCS (LNAI), vol. 2100, Springer, Heidelberg (2001)

    Google Scholar 

  54. Levy, A.Y., Rousset, M.-C.: Combining Horn rules and description logics in CARIN. Artificial Intelligence 104(1-2), 165–209 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  55. Lutz, C.: Description logics with concrete domains—a survey. In: Advances in Modal Logics, vol. 4, World Scientific Publishing Co. Pte. Ltd. (2003)

    Google Scholar 

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

    Google Scholar 

  57. Motik, B., Rosati, R.: A faithful integration of description logics with logic programming. In: IJCAI-07. Proc. of the 20th Int. Joint Conf. on Artificial Intelligence, pp. 477–482 (2007)

    Google Scholar 

  58. Motik, B., Sattler, U., Studer, R.: Query answering for OWL-DL with rules, vol. 3(1), pp. 41–60. John Wiley & Sons, Chichester (2005)

    Google Scholar 

  59. Pacholski, L., Szwast, W., Tendera, L.: Complexity results for first-order two-variable logic with counting. SIAM Journal of Computing 29(4), 1083–1117 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  60. Protégé (2003), Homepage at http://protege.stanford.edu/

  61. Rector, A., Horrocks, I.: Experience building a large, re-usable medical ontology using a description logic with transitivity and concept inclusions. In: AAAI 1997. Proc. of the WS on Ontological Engineering, AAAI Spring Symposium, AAAI Press, Stanford, California, USA (1997)

    Google Scholar 

  62. Reiter, R.: What should a database know? Journal of Logic Programming 14, 127–153 (1990)

    Article  MathSciNet  Google Scholar 

  63. Rosati, R.: Towards expressive KR systems integrating datalog and description logics: preliminary report. In: DL 1999. Proc. of the 1999 Description Logic Workshop. CEUR (1999), http://ceur-ws.org/

  64. Rosati, R.: Dl+log: Tight integration of description logics and disjunctive datalog. In: KR-06. Proc. of the 10th Int. Conf. on the Principles of Knowledge Representation and Reasoning, pp. 68–78 (2006)

    Google Scholar 

  65. Russell, S., Norvig, P.: Artificial Intelligence. A Modern Approach. Prentice-Hall, Englewood Cliffs (1995)

    MATH  Google Scholar 

  66. Schaerf, A.: Reasoning with individuals in concept languages. Data and Knowledge Engineering 13(2), 141–176 (1994)

    Article  Google Scholar 

  67. Schild, K.: A correspondence theory for terminological logics: Preliminary report. In: IJCAI-91. Proc. of the 12th Int. Joint Conf. on Artificial Intelligence, Sydney, pp. 466–471 (1991)

    Google Scholar 

  68. Schild, K.: Terminological cycles and the propositional μ-calculus. In: Doyle, J., Sandewall, E., Torasso, P. (eds.) KR-94. Proc. of the 4th Int. Conf. on the Principles of Knowledge Representation and Reasoning, Bonn, pp. 509–520. Morgan Kaufmann, Los Altos (1994)

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  70. Sirin, E., Parsia, B., Cuenca Grau, B., Kalyanpur, A., Katz, Y.: Pellet: A practical owl-dl reasoner. John Wiley & Sons, Chichester (to appear, 2007)

    Google Scholar 

  71. Spackman, K.A.: Managing clinical terminology hierarchies using algorithmic calculation of subsumption: Experience with SNOMED-RT. Journal of the American Medical Informatics Association, Fall Symposium Special Issue (2000)

    Google Scholar 

  72. Stevens, R., Horrocks, I., Goble, C., Bechhofer, S.: Building a bioinformatics ontology using OIL. IEEE Information Technology in Biomedicine. special issue on Bioinformatics 6(2), 135–141 (2002)

    Google Scholar 

  73. Sure, Y., Staab, S., Angele, J.: OntoEdit: Guiding ontology development by methodology and inferencing. In: Meersman, R., Tari, Z., et al. (eds.) CoopIS 2002, DOA 2002, and ODBASE 2002. LNCS, vol. 2519, Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  74. Uschold, M., King, M., Moralee, S., Zorgios, Y.: The enterprise ontology. The Knowledge Engineering Review 13 (1998)

    Google Scholar 

  75. Vardi, M.Y.: Why is modal logic so robustly decidable? In: Immerman, N., Kolaitis, P.G. (eds.) Descriptive Complexity and Finite Models. DIMACS: Series in Discrete Mathematics and Theoretical Computer Science, vol. 31, American Mathematical Society, Providence, RI (1997)

    Google Scholar 

  76. Wolstencroft, K., Brass, A., Horrocks, I., Lord, P., Sattler, U., Turi, D., Stevens, R.: A little semantic web goes a long way in biology. In: Gil, Y., Motta, E., Benjamins, V.R., Musen, M.A. (eds.) ISWC 2005. LNCS, vol. 3729, Springer, Heidelberg (2005)

    Chapter  Google Scholar 

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  1. University of Manchester,  

    Ulrike Sattler

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  1. Ulrike Sattler
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Grigoris Antoniou Uwe Aßmann Cristina Baroglio Stefan Decker Nicola Henze Paula-Lavinia Patranjan Robert Tolksdorf

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Sattler, U. (2007). Reasoning in Description Logics: Basics, Extensions, and Relatives. In: Antoniou, G., et al. Reasoning Web. Reasoning Web 2007. Lecture Notes in Computer Science, vol 4636. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74615-7_2

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