Skip to main content
SpringerLink
Log in

Implementation and Optimisation of a Tableau Algorithm for the Guarded Fragment

  • Conference paper
  • First Online:
Automated Reasoning with Analytic Tableaux and Related Methods (TABLEAUX 2002)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2381))

Abstract

In this paper, we present Saga, the implementation of a tableau-based Satisfiability Algorithm for the Guarded Fragment (GF). Satisfiability for GF with finite signature is ExpTime-complete and therefore theoretically intractable, but existing tableau-based systems for ExpTime-complete description and modal logics perform well for many realistic knowledge bases. We implemented and evaluated several optimisations used in description logic systems, and our results show that with an efficient combination, Saga can compete with existing highly optimised systems for description logics and first order logic.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

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.

References

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

    Article  MATH  MathSciNet  Google Scholar 

  2. A. B. Baker. Intelligent Backtracking on Constraint Satisfaction Problems: Experimental and Theoretical Results. PhD thesis, University of Oregon, 1995.

    Google Scholar 

  3. R. Dyckhoff, editor. Automated Reasoning with Analytic Tableaux and Related Methods, International Conference (TABLEAUX 2000), volume 1847 of Lecture Notes in Artificial Intelligence. Springer-Verlag, 2000.

    Google Scholar 

  4. M. J. Fischer and R. E. Ladner. Propositional dynamic logic of regular programs. Journal of Computer and System Science, 18:194–211, 1979.

    Article  MATH  MathSciNet  Google Scholar 

  5. E. Franconi, G. De Giacomo, R. M. MacGregor, W. Nutt, and C. A. Welty, editors. Proceedings of the International Workshop on Description Logics, Povo-Trento, Italy, 1998. CEUR.

    Google Scholar 

  6. J. W. Freeman. Improvements to propositional satisfiability search algorithms. PhD thesis, University of Pennsylvania, 1995.

    Google Scholar 

  7. J. W. Freeman. Hard random 3-SAT problems and the Davis-Putnam procedure. Artificial Intelligence, 81:183–198, 1996.

    Article  MathSciNet  Google Scholar 

  8. H. Ganzinger, editor. Proceedings of the 16th International Conference on Automated Deduction (CADE-99), volume 1632 of Lecture Notes in Artificial Intelligence, Berlin, 1999. Springer-Verlag.

    Google Scholar 

  9. H. Ganzinger and H. de Nivelle. A superposition decision procedure for the guarded fragment with equality. In 14th IEEE Symposium on Logic in Computer Science (LICS), Trento, Italy, 1999. IEEE Computer Society Press.

    Google Scholar 

  10. E. Grädel. Guarded fragments of first-order logic: a perspective for new description logics? In G. De Giacomo, R. M. MacGregor, W. Nutt, and C. A. Welty, editors. Proceedings of the International Workshop on Description Logics, Povo-Trento, Italy, 1998. CEUR Franconi et al. [5]. Extended abstract.

    Google Scholar 

  11. E. Grädel. Decision procedures for guarded logics. In Ganzinger [8].

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  13. V. Haarslev and R. Möller. Consistency testing: The RACE experience. In Dyckhoff [3].

    Google Scholar 

  14. V. Haarslev and R. Möller. Description of the RACER system and ist applications. In D.L. McGuinness, P.F. Patel-Schneider, C. Goble, and R. Möller, editors, Proceedings of the 2001 International Workshop on Description Logics (DL2001), volume 49, Stanford, CA, USA, 2001. CEUR.

    Google Scholar 

  15. V. Haarslev and R. Möller. High performance reasoning with very large knowledge bases: A practical case study. In Bernhard Nebel, editor, Proceedings of the Seventeenth International Joint Conference on Aritificial Intelligence. Morgan Kaufman Publishers, San Francisco, USA, 2001.

    Google Scholar 

  16. V. Haarslev, R. Möller, and A.-Y. Turhan. RACE user’s guide and reference manual version 1.1. Technical Report FBI-HH-M-289/99, University of Hamburg, CS department, 1999.

    Google Scholar 

  17. C. Hirsch and S. Tobies. A tableau algorithm for the clique guarded fragment. In F. Wolter, H. Wansing, M. de Rijke, and M. Zakharyaschev, editors, Advances in Modal Logics, volume 3, Stanford, 2001. CSLI Publications.

    Google Scholar 

  18. J. Hladik. Implementing the n-ary description logic GF1−. In F. Baader and U. Sattler, editors, Proceedings of the International Workshop on Description Logics, Aachen, Germany, 2000. CEUR.

    Google Scholar 

  19. I. Horrocks. Optimising Tableaux Decision Procedures for Description Logics. PhD thesis, University of Manchester, 1997.

    Google Scholar 

  20. I. Horrocks. Using an expressive description logic: FaCT or fiction? In A. G. Cohn, L. Schubert, and S. C. Shapiro, editors, Principles of Knowledge Representation and Reasoning: Proceedings of the Sixth International Conference (KR’98). Morgan Kaufmann Publishers, San Francisco, California, 1998.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  23. I. Horrocks, U. Sattler, and S. Tobies. Practical reasoning for expressive description logics. In H. Ganzinger, D. McAllester, and A. Voronkov, editors, Proceedings of the Sixth International Conference on Logic for Programming and Automated Reasoning (LPAR’99), number 1705 in Lecture Notes in Artificial Intelligence, pages 161–180. Springer-Verlag, 1999.

    Google Scholar 

  24. U. Hustadt, R. A. Schmidt, and C. Weidenbach. MSPASS: Subsumption testing with SPASS. In A. Borgida, M. Lenzerini, R. Möller, and P. Patel-Schneider, editors. Proceedings of the International Workshop on Description Logics, Linköping, Sweden, 1999. CEUR Lambrix et al. [25].

    Google Scholar 

  25. P. Lambrix, A. Borgida, M. Lenzerini, R. Möller, and P. Patel-Schneider, editors. Proceedings of the International Workshop on Description Logics, Linköping, Sweden, 1999. CEUR.

    Google Scholar 

  26. C. Lutz, U. Sattler, and S. Tobies. A suggestion for an n-ary description logic. In A. Borgida, M. Lenzerini, R. Möller, and P. Patel-Schneider, editors. Proceedings of the International Workshop on Description Logics, Linköping, Sweden, 1999. CEUR Lambrix et al. [25].

    Google Scholar 

  27. F. Massacci and F. M. Donini. Design and results of TANCS-2000. In Dyckhoff [3].

    Google Scholar 

  28. P. F. Patel-Schneider. DLP system description. In G. De Giacomo, R. M. MacGregor, W. Nutt, and C. A. Welty, editors. Proceedings of the International Workshop on Description Logics, Povo-Trento, Italy, 1998. CEUR Franconi et al. [5].

    Google Scholar 

  29. V. R. Pratt. Models of program logics. In Proceedings of the 20th Annual Symposium on Foundations of Computer Science, San Juan, Puerto Rico, 1979.

    Google Scholar 

  30. C. Weidenbach. SPASS: Combining superposition, sorts and splitting. In A. Robinson and A. Voronkov, editors, Handbook of Automated Reasoning, chapter 27. Elsevier, 1999.

    Google Scholar 

  31. C. Weidenbach, B. Afshordel, U. Brahm, C. Cohrs, T. Engel, E. Keen, C. Theobalt, and D. Topić. System description: SPASS version 1.0.0. In Ganzinger [8].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theoretical Computer Science, TU Dresden, Germany

    Jan Hladik

Authors
  1. Jan Hladik
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Abteilung Wisssenbasierte Systeme 184/3, Technische Univesität Wien, Favoritenstr. 9-11, 1040, Vienna, Austria

    Uwe Egly

  2. Institut für Computersprachen AG Theoretische Informatik und Logik 185.2, Technische Universität Wien, Favoritenstr. 9-11, 1040, Vienna, Austria

    Chritian G. Fermüller

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hladik, J. (2002). Implementation and Optimisation of a Tableau Algorithm for the Guarded Fragment. In: Egly, U., Fermüller, C.G. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2002. Lecture Notes in Computer Science(), vol 2381. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45616-3_11

Download citation

  • DOI: https://doi.org/10.1007/3-540-45616-3_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43929-5

  • Online ISBN: 978-3-540-45616-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation