Skip to main content
Springer Nature Link
Log in

Tableaux with Global Caching for Checking Satisfiability of a Knowledge Base in the Description Logic \(\mathcal{SH}\)

  • Conference paper
Transactions on Computational Collective Intelligence I

Part of the book series: Lecture Notes in Computer Science ((TCCI,volume 6220))

  • 391 Accesses

Abstract

Description logics (DLs) are a family of knowledge representation languages which can be used to represent the terminological knowledge of an application domain in a structured and formally well-understood way. DLs can be used, for example, for conceptual modeling or as ontology languages. In fact, OWL (Web Ontology Language), recommended by W3C, is based on description logics.

In the current paper we give the first direct ExpTime (optimal) tableau decision procedure, which is not based on transformation or on the pre-completion technique, for checking satisfiability of a knowledge base in the description logic \(\mathcal{SH}\). Our procedure uses sound global caching and can be implemented as an extension of the highly optimized tableau prover TGC to obtain an efficient program for the mentioned satisfiability problem.

Supported by grants N N206 399134 and N N206 370739 from the Polish Ministry of Science and Higher Education.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. Donini, F., Massacci, F.: ExpTime tableaux for \(\mathcal{ALC}\). Artificial Intelligence 124, 87–138 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. De Giacomo, G.: Decidability of Class-Based Knowledge Representation Formalisms. PhD thesis, Universita’ di Roma “La Sapienza” (1995)

    Google Scholar 

  4. De Giacomo, G., Lenzerini, M.: TBox and ABox reasoning in expressive description logics. In: Aiello, L.C., Doyle, J., Shapiro, S.C. (eds.) Proc. of KR’1996, pp. 316–327. Morgan Kaufmann, San Francisco (1996)

    Google Scholar 

  5. Goré, R.: Tableau methods for modal and temporal logics. In: D’Agostino, et al. (eds.) Handbook of Tableau Methods, pp. 297–396. Kluwer, Dordrecht (1999)

    Google Scholar 

  6. Goré, R., Nguyen, L.A.: ExpTime tableaux for \(\mathcal{ALC}\) using sound global caching. In: Calvanese, D., et al. (eds.) Proc. of DL 2007, pp. 299–306 (2007)

    Google Scholar 

  7. Goré, R., Nguyen, L.A.: ExpTime tableaux with global caching for description logics with transitive roles, inverse roles and role hierarchies. In: Olivetti, N. (ed.) TABLEAUX 2007. LNCS (LNAI), vol. 4548, pp. 133–148. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Hollunder, B.: Consistency checking reduced to satisfiability of concepts in terminological systems. Ann. Math. Artif. Intell. 18(2-4), 133–157 (1996)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  10. Horrocks, I., Sattler, U.: Description logics - basics, applications, and more. In: Tutorial given at ECAI 2002 (2002), http://www.cs.man.ac.uk/~horrocks/Slides/ecai-handout.pdf

  11. 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  MathSciNet  Google Scholar 

  12. Horrocks, I., Sattler, U., Tobies, S.: Reasoning with individuals for the description logic SHIQ. In: McAllester, D. (ed.) CADE 2000. LNCS, vol. 1831, pp. 482–496. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  13. Nguyen, L.A.: Analytic tableau systems and interpolation for the modal logics KB, KDB, K5, KD5. Studia Logica 69(1), 41–57 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  14. Nguyen, L.A.: An efficient tableau prover using global caching for the description logic ALC. Fundamenta Informaticae 93(1-3), 273–288 (2009)

    MATH  MathSciNet  Google Scholar 

  15. Nguyen, L.A., Szałas, A.: Checking consistency of an ABox w.r.t. global assumptions in PDL. In: Czaja, L., Szczuka, M. (eds.) Proc. of CS&P’2009, pp. 431–442 (2009)

    Google Scholar 

  16. Nguyen, L.A., Szałas, A.: EXPTIME tableaux for checking satisfiability of a knowledge base in the description logic ALC. In: Nguyen, N.T., Kowalczyk, R., Chen, S.-M. (eds.) ICCC 2009. LNCS (LNAI), vol. 5796, pp. 437–448. Springer, Heidelberg (2009)

    Google Scholar 

  17. Nguyen, L.A., Szałas, A.: An optimal tableau decision procedure for Converse-PDL. In: Nguyen, N.-T., Bui, T.-D., Szczerbicki, E., Nguyen, N.-B. (eds.) Proc. of KSE’2009, pp. 207–214. IEEE Computer Society, Los Alamitos (2009)

    Google Scholar 

  18. Nguyen, L.A., Szałas, A.: A tableau calculus for regular grammar logics with converse. In: Schmidt, R.A. (ed.) Automated Deduction – CADE-22. LNCS (LNAI), vol. 5663, pp. 421–436. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  19. Pratt, V.R.: A near-optimal method for reasoning about action. J. Comput. Syst. Sci. 20(2), 231–254 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  20. Rautenberg, W.: Modal tableau calculi and interpolation. JPL 12, 403–423 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  21. Schild, K.: A correspondence theory for terminological logics: Preliminary report. In: Mylopoulos, J., Reiter, R. (eds.) Proc. of IJCAI’1991, pp. 466–471. Morgan Kaufmann, San Francisco (1991)

    Google Scholar 

  22. Tobies, S.: Complexity results and practical algorithms for logics in knowledge representation. PhD thesis, RWTH-Aachen (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Informatics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Linh Anh Nguyen & Andrzej Szałas

  2. Dept. of Computer and Information Science, Linköping University, SE-581 83, Linköping, Sweden

    Andrzej Szałas

Authors
  1. Linh Anh Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrzej Szałas
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute of Informatics, Wroclaw University of Technology, Str. Wyb. Wyspianskiego 27, 50-370, Wroclaw, Poland

    Ngoc Thanh Nguyen

  2. Centre for Complex Software Systems and Services, Swinburne University of Technology, P.O. Box 218, 3122, Hawthorn, Victoria, Australia

    Ryszard Kowalczyk

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nguyen, L.A., Szałas, A. (2010). Tableaux with Global Caching for Checking Satisfiability of a Knowledge Base in the Description Logic \(\mathcal{SH}\) . In: Nguyen, N.T., Kowalczyk, R. (eds) Transactions on Computational Collective Intelligence I. Lecture Notes in Computer Science, vol 6220. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15034-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-15034-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15033-3

  • Online ISBN: 978-3-642-15034-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics