Skip to main content
SpringerLink
Log in

Propositional Temporal Proving with Reductions to a SAT Problem

  • Conference paper
Automated Deduction – CADE-24 (CADE 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7898))

Included in the following conference series:

Abstract

We present a new approach to reasoning in propositional linear-time temporal logic (PLTL). The method is based on the simplified temporal resolution calculus. We prove that the search for premises to apply the rules of simplified temporal resolution can be re-formulated as a search for minimal unsatisfiable subsets (MUS) in a set of classical propositional clauses. This reformulation reduces a large proportion of PLTL reasoning to classical propositional logic facilitating the use of modern tools. We describe an implementation of the method using the CAMUS system for MUS computation and present an in-depth comparison of the performance of the new solver against a clausal temporal resolution prover.

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. Belov, A., Lynce, I., Marques-Silva, J.: Towards efficient MUS extraction. AI Commun. 25(2), 97–116 (2012)

    MathSciNet  MATH  Google Scholar 

  2. Biere, A.: Bounded model checking. In: Handbook of Satisfiability. Frontiers in Artificial Intelligence and Applications, vol. 185, pp. 457–481. IOS Press (2009)

    Google Scholar 

  3. Bloem, R., Galler, S., Jobstmann, B., Piterman, N., Pnueli, A., Weiglhofer, M.: Automatic hardware synthesis from specifications: A case study. In: Proceedings of DATE 2007, pp. 1–6. IEEE (2007)

    Google Scholar 

  4. Bradley, A.R.: SAT-based model checking without unrolling. In: Jhala, R., Schmidt, D. (eds.) VMCAI 2011. LNCS, vol. 6538, pp. 70–87. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  5. Claessen, K., Sörensson, N.: A liveness checking algorithm that counts. In: Proceedings of FMCAD 2012, pp. 52–59. IEEE (2012)

    Google Scholar 

  6. Clarke, E.M., Grumberg, O., Peled, D.A.: Model checking. MIT Press (1999)

    Google Scholar 

  7. Degtyarev, A., Fisher, M., Konev, B.: A simplified clausal resolution procedure for propositional linear-time temporal logic. In: Egly, U., Fermüller, C. (eds.) TABLEAUX 2002. LNCS (LNAI), vol. 2381, pp. 85–99. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  8. Degtyarev, A., Fisher, M., Konev, B.: Monodic temporal resolution. ACM Trans. Comput. Log. 7(1), 108–150 (2006)

    Article  MathSciNet  Google Scholar 

  9. Dixon, C.: Using Otter for temporal resolution. In: Advances in Temporal Logic, pp. 149–166. Kluwer (2000)

    Google Scholar 

  10. Dixon, C., Konev, B., Fisher, M., Nietiadi, S.: Deductive temporal reasoning with constraints. Journal of Applied Logic (2012)

    Google Scholar 

  11. Fisher, M., Dixon, C., Peim, M.: Clausal temporal resolution. ACM Transactions on Computational Logic 2(1), 12–56 (2001)

    Article  MathSciNet  Google Scholar 

  12. Fisman, D., Kupferman, O., Sheinvald-Faragy, S., Vardi, M.Y.: A framework for inherent vacuity. In: Chockler, H., Hu, A.J. (eds.) HVC 2008. LNCS, vol. 5394, pp. 7–22. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  13. Giunchiglia, E., Tacchella, A., Giunchiglia, F.: SAT-based decision procedures for classical modal logics. J. Autom. Reasoning 28(2), 143–171 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. Giunchiglia, F., Sebastiani, R.: A SAT-based decision procedure for ALC. In: Proceedings of KR 1996, pp. 304–314. Morgan Kaufmann (1996)

    Google Scholar 

  15. Halpern, J.Y., van der Meyden, R., Vardi, M.Y.: Complete axiomatizations for reasoning about knowledge and time. SIAM J. Comput. 33(3), 674–703 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  16. Hébert, C., Bretto, A., Crémilleux, B.: A data mining formalization to improve hypergraph minimal transversal computation. Fundamenta Informaticae 80(4), 415–433 (2007)

    MathSciNet  MATH  Google Scholar 

  17. Hustadt, U., Konev, B.: TRP++ 2.0: A temporal resolution prover. In: Baader, F. (ed.) CADE 2003. LNCS (LNAI), vol. 2741, pp. 274–278. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  18. Hustadt, U., Schmidt, R.A.: Scientific benchmarking with temporal logic decision procedures. In: Proceedings of KR 2002, pp. 533–546. Morgan Kaufmann (2002)

    Google Scholar 

  19. Liffiton, M.H., Sakallah, K.A.: Algorithms for computing minimal unsatisfiable subsets of constraints. Journal of Automated Reasoning 40(1), 1–33 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  20. Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems: Specification. Springer (1992)

    Google Scholar 

  21. Marques-Silva, J.: Computing minimally unsatisfiable subformulas: State of the art and future directions. Multiple-Valued Logic and Soft Computing 19(1-3), 163–183 (2012)

    MathSciNet  Google Scholar 

  22. Murakami, K., Uno, T.: Efficient algorithms for dualizing large-scale hypergraphs. CoRR abs/1102.3813 (2011)

    Google Scholar 

  23. Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: Proceedings POPL 1989, pp. 179–190. ACM (1989)

    Google Scholar 

  24. Rozier, K., Vardi, M.: LTL satisfiability checking. International Journal on Software Tools for Technology Transfer 12(2), 123–137 (2010)

    Article  Google Scholar 

  25. Schuppan, V., Darmawan, L.: Evaluating LTL satisfiability solvers. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 397–413. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  26. Suda, M., Weidenbach, C.: A PLTL-prover based on labelled superposition with partial model guidance. In: Gramlich, B., Miller, D., Sattler, U. (eds.) IJCAR 2012. LNCS, vol. 7364, pp. 537–543. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  27. Tansel, A.U., Clifford, J., Gadia, S.K., Jajodia, S., Segev, A., Snodgrass, R.T.: Temporal Databases: Theory, Design, and Implementation. Benjamin/Cummings (1993)

    Google Scholar 

  28. Vardi, M.Y., Wolper, P.: Automata-theoretic techniques for modal logics of programs. Journal of Computer and System Sciences 32(2), 183–219 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  29. Williams, R., Konev, B.: Simplified temporal resolution using SAT solvers. In: Proceedings of ARW 2012, pp. 9–10. The University of Manchester (2012)

    Google Scholar 

  30. Wolper, P.: The tableau method for temporal logic: An overview. Logique et Analyse 28, 119–152 (1985)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Liverpool, Liverpool, L69 7ZF, UK

    Richard Williams & Boris Konev

Authors
  1. Richard Williams
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Boris Konev
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Verona, Strada Le Grazie 15, 37134, Verona, Italy

    Maria Paola Bonacina

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Williams, R., Konev, B. (2013). Propositional Temporal Proving with Reductions to a SAT Problem. In: Bonacina, M.P. (eds) Automated Deduction – CADE-24. CADE 2013. Lecture Notes in Computer Science(), vol 7898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38574-2_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-38574-2_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38573-5

  • Online ISBN: 978-3-642-38574-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation