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Implementing Tableau Calculi Using BDDs: BDDTab System Description

  • Rajeev Goré
  • Kerry Olesen
  • Jimmy Thomson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8562)

Abstract

We present a modification of the DPLL-based approach to decide modal satisfiability where we substitute DPLL by BDDs. We demonstrate our method by implementing the standard tableau calculi for automated reasoning in propositional modal logics K and S4, along with extensions to the multiple modalities of \(\mathcal{ALC}\). We evaluate our implementation of such a reasoner using several K and S4 benchmark sets, as well as some \(\mathcal{ALC}\) ontologies. We show, with comparison to FaCT++, InKreSAT and *SAT, that it can compete with other state of the art methods of reasoning in propositional modal logic. We also discuss how this technique extends to tableau for other propositional logics.

Keywords

Description Logic Automate Reasoning Saturation Phase Modal Formula Classical Propositional Logic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Barrett, C.W., Sebastiani, R., Seshia, S.A., Tinelli, C.: Satisfiability modulo theories. In: Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 825–885. IOS Press (2009)Google Scholar
  2. 2.
  3. 3.
    Giunchiglia, F., Sebastiani, R.: Building decision procedures for modal logics from propositional decision procedures - the case study of modal K(m). Information and Computation 162(1/2) (October/November 2000)Google Scholar
  4. 4.
    Goré, R., Thomson, J.: BDD-based automated reasoning for propositional bi-intuitionistic tense logics. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 301–315. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  5. 5.
    Heuerding, A., Schwendimann, S.: A benchmark method for the propositional modal logics K, KT, S4 (1996)Google Scholar
  6. 6.
    Horrocks, I., Patel-Schneider, P.F.: Optimizing Description Logic Subsumption. Journal of Logic and Computation 9(3), 267–293 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Kaminski, M., Tebbi, T.: Inkresat: Modal reasoning via incremental reduction to SAT. In: Bonacina, M.P. (ed.) CADE 2013. LNCS, vol. 7898, pp. 436–442. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  8. 8.
    Massacci, F., Donini, F.M.: Design and results of TANCS-2000 non-classical (modal) systems comparison. In: Dyckhoff, R. (ed.) TABLEAUX 2000. LNCS, vol. 1847, pp. 52–56. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  9. 9.
    Sebastiani, R., Tacchella, A.: SAT techniques for modal and description logics. In: Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 781–824. IOS Press (2009)Google Scholar
  10. 10.
    Sebastiani, R., Vescovi, M.: Automated Reasoning in Modal and Description Logics via SAT Encoding: the Case Study of K(m)/ALC-Satisfiability. Journal of Artificial Intelligence Research (JAIR) 35, 343–389 (2009)zbMATHMathSciNetGoogle Scholar
  11. 11.
    Tacchella, A.: *sat system description. In: Description Logics (1999)Google Scholar
  12. 12.
    Tsarkov, D., Horrocks, I.: Fact++ description logic reasoner: System description. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 292–297. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Rajeev Goré
    • 1
  • Kerry Olesen
    • 1
  • Jimmy Thomson
    • 1
  1. 1.Research School of Computer ScienceAustralian National UniversityAustralia

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