Skip to main content
Log in

Optimizing Terminological Reasoning for Expressive Description Logics

  • Published:
Journal of Automated Reasoning Aims and scope Submit manuscript

Abstract

Tableau algorithms are currently the most widely used and empirically the fastest algorithms for reasoning in expressive description logics, including the important description logics \(\mathcal{SHIQ}\) and \(\mathcal{SHOIQ}\). Achieving a high level of performance on terminological reasoning in expressive description logics when using tableau-based algorithms requires the incorporation of a wide variety of optimizations. The description logic system FaCT++ implements a wide variety of such optimizations, some present in other reasoners and some novel or refined in FaCT++.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Baader, F., Brandt, S., Lutz, C.: Pushing the \(\mathcal{EL}\) envelope. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI 2005), Edinburgh, 30 July–5 August (2005)

  2. 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 

  3. 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 (special issue on Knowledge Base Management). Appl. Artif. Intell. 4, 109–132 (1994)

    Google Scholar 

  4. Baader, F. Sattler, U.: An overview of tableau algorithms for description logics. Stud. Log. 69(1), 5–40 (2001)

    Article  MATH  Google Scholar 

  5. Baker, A.B.: Intelligent backtracking on constraint satisfaction problems: experimental and theoretical results. Ph.D. thesis, University of Oregon (1995)

  6. Calvanese, D., De Giacomo, G., Lenzerini, M.: On the decidability of query containment under constraints. In: Proceedings of the 17th ACM SIGACT SIGMOD SIGART Symposium on Principles of Database Systems (PODS98), pp. 149–158 (1998)

  7. Calvanese, D., De Giacomo, G., Lenzerini, M., Nardi, D., Rosati, R.: Description logic framework for information integration. In: Proceedings of the 6th Internationa Conference on Principles of Knowledge Representation and Reasoning (KR98), pp. 2–13 (1998)

  8. Chen, C., Haarslev, V., Wang, J.: LAS: extending Racer by a large Abox store. In: Proceedings of the 2005 International Workshop on Description Logics (DL-2005), pp. 200–207. Edinburgh, 26–28 July 2005

  9. Davis, M., Logemann, G., Loveland, D.: A machine program for theorem proving. Commun. ACM 5, 394–397 (1962)

    Article  MATH  Google Scholar 

  10. Davis, M., Putnam, H.: A computing procedure for quantification theory. J. Assoc. Comput. Mach. 7(3), 201–215 (1960)

    MATH  Google Scholar 

  11. Ding, Y., Haarslev, V.: Towards efficient reasoning for description logics with inverse roles. In: Proceedings of the 2005 International Workshop on Description Logics (DL-2005), pp. 208–215. Edinburgh, 26–28 July 2005

  12. Ding, Y., Haarslev, V.: Tableau caching for description logics with inverse and transitive roles. In: Proceedings of the 2006 International Workshop on Description Logics (DL-2006), Lake District (2006)

  13. Fensel, D., van Harmelen, F., Horrocks, I., McGuinness, D., Patel-Schneider, P.F.: OIL: an ontology infrastructure for the semantic web. IEEE Intell. Syst. 16(2), 38–45 (2001)

    Article  Google Scholar 

  14. Freeman, J.W.: Improvements to propositional satisfiability search algorithms. Ph.D. thesis, Department of Computer and Information Science, University of Pennsylvania (1995)

  15. Giunchiglia, E., Tacchella, A.: A subset-matching size-bounded cache for satisfiability in modal logics. In: Proceedings of the 4th International Conference on Analytic Tableaux and Related Methods (TABLEAUX 2000), pp. 237–251. Springer, Berlin Heidelberg New York (2000)

    Chapter  Google Scholar 

  16. Giunchiglia, F., Sebastiani, R.: Building decision procedures for modal logics from propositional decision procedures—the case study of modal K. In: McRobbie M.A., Slaney J.K. (eds.) Proceedings of the 13th International Conference on Automated Deduction (CADE96), vol. 1104 of Lecture Notes in Artificial Intelligence, pp. 583–597. Springer, Berlin Heidelberg New York (1996)

    Google Scholar 

  17. Haarslev, V., Möller, R.: Expressive ABox reasoning with number restrictions, role hierarchies, and transitively closed roles. In: Proceedings of the 7th International Conference on Principles of Knowledge Representation and Reasoning (KR 2000), pp. 273–284 (2000)

  18. Haarslev, V., Möller, R.: High performance reasoning with very large knowledge bases: a practical case study. In: Proceedings of the 17th International Joint Conference on Artificial Intelligence (IJCAI 2001), pp. 161–168 (2001)

  19. Haarslev, V., Möller, R.: Optimizing reasoning in description logics with qualified number restrictions. In: Proceedings of the 2001 Description Logic Workshop (DL 2001), pp. 142–151. CEUR Electronic Workshop Proceedings. http://ceur-ws.org/Vol-49/ (2001)

  20. Haarslev, V., Möller, R.: Racer: a core inference engine for the semantic web. In: Proceedings of the 2nd InternationalWorkshop on Evaluation of Ontology-based Tools (EON2003), pp. 27–36. Sanibel Island, FL (2003)

  21. Haarslev, V., Möller, R.: Optimization techniques for retrieving resources described in OWL/RDF documents: first results. In: Ninth International Conference on the Principles of Knowledge Representation and Reasoning, KR 2004, pp. 163–173. Whistler, 2–5 June 2004

  22. Haarslev, V., Möller, R., Turhan, A.: Exploiting pseudo models for TBox and ABox reasoning in expressive description logics. In: Goré, R., Leitsch, A., Nipkow, T. (eds.) International Joint Conference on Automated Reasoning, IJCAR2001, 18–23 June, Siena, pp. 29–44. Springer, Berlin Heidelberg New York (2001)

    Google Scholar 

  23. Haarslev, V., Möller, R., Wessel, M.: Description logic inference technology: lessons learned in the trenches. In: Horrocks, I., Sattler, U., Wolter, F. (eds.) Proceedings of the International Workshop on Description Logics (2005)

  24. Haarslev, V., Timmann, M., Möller, R.: Combining tableaux and algebraic methods for reasoning with qualified number restrictions. In: Proceedings of the International Workshop on Description Logics (DL-2001), pp. 152–161. Stanford, 1–3 August 2001

  25. Hladik, J.: Implementation and optimisation of a tableau algorithm for the guarded fragment. In: Egly, U., Fermüller C.G. (eds.) Proceedings of the International Conference on Automated Reasoning with Tableaux and Related Methods (Tableaux 2002), vol. 2381 of Lecture Notes in Artificial Intelligence. Springer, Berlin Heidelberg New York (2002)

    Google Scholar 

  26. Hoffmann, J., Koehler, J.: A new method to index and query sets. In: Proceedings of the 16th International Joint Conference on Artificial Intelligence (IJCAI99), pp. 462–467 (1999)

  27. Horrocks, I.: Optimising tableaux decision procedures for description logics. Ph.D. thesis, University of Manchester (1997)

  28. Horrocks, I.: Using an expressive description logic: fact or fiction?. In: Proceedings of the 6th International Conference on Principles of Knowledge Representation and Reasoning (KR98), pp. 636–647 (1998)

  29. Horrocks, I.: Implementation and optimisation techniques. In: Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider, P.F. (eds.) The Description Logic Handbook: Theory, Implementation, and Applications. pp. 306–346. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  30. Horrocks, I., Hustadt, U., Sattler, U., Schmidt, R.: Computational modal logic. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic. Elsevier, Amsterdam (2006)

    Google Scholar 

  31. Horrocks, I., Patel-Schneider, P.F.: DL systems comparison. In: Proceedings of the 1998 Description Logic Workshop (DL’98), vol. 11 of CEUR (http://ceur-ws.org/), pp. 55–57 (1998)

  32. Horrocks, I., Patel-Schneider, P.F.: Optimizing description logic subsumption. J. Log. Comput. 9(3), 267–293 (1999)

    Article  MATH  Google Scholar 

  33. Horrocks, I., Patel-Schneider, P.F.: Reducing OWL entailment to description logic satisfiability. In: Fensel, D., Sycara, K., Mylopoulos, J. (eds.) Proceedings of the 2003 International Semantic Web Conference (ISWC 2003), pp. 17–29. Springer, Berlin Heidelberg New York (2003)

    Google Scholar 

  34. Horrocks, I., Patel-Schneider, P.F., Bechhofer, S., Tsarkov, D.: OWL rules: a proposal and prototype implementation. J. Web Semantics 3(1), 23–40 (2005)

    Google Scholar 

  35. Horrocks, I., Patel-Schneider, P.F., van Harmelen, F.: Reviewing the design of DAML+OIL: an ontology language for the semantic web. In: Proceedings of the 18th National Conference on Artificial Intelligence (AAAI 2002), pp. 792–797. AAAI Press, Menlo Park (2002)

    Google Scholar 

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

    Google Scholar 

  37. Horrocks, I., Sattler, U.: A description logic with transitive and inverse roles and role hierarchies. J. Log. Comput. 9(3), 385–410 (1999)

    Article  MATH  Google Scholar 

  38. Horrocks, I., Sattler, U.: Optimised reasoning for \(\mathcal{SHIQ}\). In: Proceedings of the 15th European Conference on Artificial Intelligence (ECAI 2002), pp. 277–281 (2002)

  39. Horrocks, I., Sattler, U.: A tableaux decision procedure for \(\mathcal{SHOIQ}\). In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI 2005), pp. 448–453 (2005)

  40. Horrocks, I., Sattler, U., Tobies, S.: Practical reasoning for expressive description logics. In: Ganzinger, H., McAllester, D., Voronkov, A. (eds.) Proceedings of the 6th International Conference on Logic for Programming and Automated Reasoning (LPAR’99), pp. 161–180. Springer, Berlin Heidelberg New York (1999)

    Chapter  Google Scholar 

  41. Horrocks, I., Sattler, U., Tobies, S.: Reasoning with individuals for the description logic \(\mathcal{SHIQ}\). In: McAllester, D. (ed.) Proceedings of the 17th International Conference on Automated Deduction (CADE 2000), vol. 1831 of Lecture Notes in Computer Science, pp. 482–496. Springer, Berlin Heidelberg New York (2000)

    Google Scholar 

  42. Horrocks, I., Tobies, S.: Optimisation of terminological reasoning. In: Proceedings of the 2000 Description Logic Workshop (DL 2000). pp. 183–192 (2000)

  43. Horrocks, I., Tobies, S.: Reasoning with axioms: theory and practice. In: Proceedings of the 7th International Conference on Principles of Knowledge Representation and Reasoning (KR 2000), pp. 285–296 (2000)

  44. Hudek, A.K., Weddell, G.: Binary absorption in tableaux-based reasoning for description logics. In: Proceedings of the 2006 Description Logic Workshop (DL 2006), vol. 189. CEUR (http://ceur-ws.org/) (2006)

  45. Hustadt, U., Motik, B., Sattler, U.: Reducing SHIQ-description logic to disjunctive datalog programs. In: Proceedings of the 9th International Conference on Principles of Knowledge Representation and Reasoning (KR 2004), pp. 152–162 (2004)

  46. Hustadt, U., Schmidt, R.A.: MSPASS: modal reasoning by translation and first-order resolution. In: Dyckhoff, R. (ed.) Automated Reasoning with Analytic Tableaux and Related Methods, International Conference (TABLEAUX 2000), vol. 1847 of Lecture Notes in Artificial Intelligence, pp. 67–71. Springer, Berlin Heidelberg New York (2000)

    Chapter  Google Scholar 

  47. Hustadt, U., Schmidt, R.A., Weidenbach, C.: MSPASS: subsumption testing with SPASS. In: Lambrix, P., Borgida, A., Lenzerini, M., Möller, R., Patel-Schneider P. (eds.) Proceedings of the International Workshop on Description Logics 99, pp. 136–137. Linköping University, Linköping (1999)

    Google Scholar 

  48. Kalyanpur, A., Parsia, B., Hendler, J.: A tool for working with web ontologies. Int. J. Semantic Web Information Systems 1(1), 36–49 (2005)

    Google Scholar 

  49. Kazakov, Y., Motik, B.: A resolution-based decision procedure for \(\mathcal{SHOIQ}\). In: Proceedings of the International Joint Conference on Automated Reasoning (IJCAR 2006), vol. 4130 of Lecture Notes in Artificial Intelligence, pp. 662–677. Springer, Berlin Heidelberg New York (2006)

    Google Scholar 

  50. Knublauch, H., Fergerson, R., Noy, N., Musen, M.: The Protégé OWL Plugin: an open development environment for semantic web applications. In: McIlraith, S.A., Plexousakis, D., van Harmelen, F. (eds.) Proceedings of the 2004 International Semantic Web Conference (ISWC 2004), pp. 229–243. Springer, Berlin Heidelberg New York (2004)

    Google Scholar 

  51. Lutz, C.: Complexity of terminological reasoning revisited. In: Proceedings of the 6th Interational Conference on Logic for Programming and Automated Reasoning (LPAR’99), vol. 1705 of Lecture Notes in Artificial Intelligence, pp. 181–200. Springer, Berlin Heidelberg New York  (1999)

    Google Scholar 

  52. Massacci, F.: TANCS non classical system comparison. In: Proceedings of the 3rd International Conference on Analytic Tableaux and Related Methods (TABLEAUX’99), vol. 1617 of Lecture Notes in Artificial Intelligence (1999)

  53. McGuinness, D.L., Wright, J.R.: An industrial strength description logic-based configuration platform. IEEE Intell. Syst. 69–77. (1998)

  54. Möller, R.: Expressive description logics: foundations for practical applications. Habilitation Thesis, University of Hamburg, Computer Science Department (2001)

  55. Oppacher, F., Suen, E.: HARP: a tableau-based theorem prover. J. Autom. Reason. 4, 69–100 (1988)

    Article  Google Scholar 

  56. Pan, Z.: Benchmarking DL reasoners using realistic ontologies. In: Proceedings of the First OWL Experiences and Directions Workshop (2005)

  57. Rector, A.: Medical informatics. In: Baader, F., Calvanese, D., McGuinness, D., Nardi, D., Patel-Schneider P.F. (eds.) The Description Logic Handbook: Theory, Implementation, and Applications, pp. 415–435. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  58. Rogers, J.E., Roberts, A., Solomon, W.D., van der Haring, E., Wroe, C.J., Zanstra, P.E., Rector, A.L.: GALEN Ten years on: tasks and supporting tools. In: Proceedings of MEDINFO2001, pp. 256–260 (2001)

  59. Schmidt-Schauß, M., Smolka, G.: Attributive concept descriptions with complements. Artif. Intell. 48(1), 1–26 (1991)

    Article  MATH  Google Scholar 

  60. Sirin, E., Grau, B.C., Parsia, B.: Optimizing description logic reasoning for nominals: first results. Technical report, University of Maryland Institute for Advanced Computes Studies (UMIACS), 2005-64. http://www.mindswap.org/papers/OptimizeReport.pdf. (2005)

  61. Sirin, E., Grau, B.C., Parsia, B.: From wine to water: optimizing description logic reasoning for nominals. In: International Conference on the Principles of Knowledge Representation and Reasoning (KR-2006) (2006)

  62. Sirin, E., Parsia, B., Cuenca Grau, B., Kalyanpur, A., Katz, Y.: Pellet: a practical OWL-DL reasoner. J. Web Semantics 5(2), 51–53 (2007)

  63. Stevens, R., Goble, C., Horrocks, I., Bechhofer, S.: Building a bioinformatics ontology using OIL. IEEE Trans. Inf. Technol. Biomed. 6(2), 135–141 (2002)

    Article  Google Scholar 

  64. Suntisrivaraporn, B., Baader, F., Lutz, C.: CEL—A practical reasoner for life science ontologies. In: Proceedings of the International Joint Conference on Automated Reasoning (IJCAR 2006) (2006)

  65. Tsarkov, D., Horrocks, I.: Efficient reasoning with range and domain constraints. In: Proceedings of the 2004 Description Logic Workshop (DL 2004), pp. 41–50 (2004)

  66. Tsarkov, D., Horrocks, I.: Optimised classification for taxonomic knowledge bases. In: Proceedings of the 2005 Description Logic Workshop (DL 2005), vol. 147 of CEUR (http://ceur-ws.org/) (2005)

  67. Tsarkov, D., Horrocks, I.: Ordering heuristics for description logic reasoning. In: Proceedings of the 19th International Joint Conference on Artificial Intelligence (IJCAI 2005), pp. 609–614 (2005)

  68. Tsarkov, D., Horrocks, I.: FaCT++ description logic reasoner: system description. In: Proceedings of the International Joint Conference on Automated Reasoning (IJCAR 2006), vol. 4130 of Lecture Notes in Artificial Intelligence, pp. 292–297. Springer, Berlin Heidelberg New York (2006)

    Google Scholar 

  69. Tsarkov, D., Riazanov, A., Bechhofer, S., Horrocks, I.: Using Vampire to reason with OWL. In: McIlraith, S.A., Plexousakis, D., van Harmelen F. (eds.) Proceedings of the 2004 International Semantic Web Conference (ISWC 2004), pp. 471–485. Springer, Berlin Heidelberg New York (2004)

    Google Scholar 

  70. Wolstencroft, K., Brass, A., Horrocks, I., Lord, P., Sattler, U., Stevens, R., Turi, D.: A little semantic web goes a long way in biology. In: Proceedings of the 2005 International Semantic Web Conference (ISWC 2005), pp. 786–800. Springer, Berlin Heidelberg New York (2005)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ian Horrocks.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tsarkov, D., Horrocks, I. & Patel-Schneider, P.F. Optimizing Terminological Reasoning for Expressive Description Logics. J Autom Reasoning 39, 277–316 (2007). https://doi.org/10.1007/s10817-007-9077-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10817-007-9077-y

Keywords

Navigation