SAT-Based BMC for Deontic Metric Temporal Logic and Deontic Interleaved Interpreted Systems

  • Bożena Woźna-Szcześniak
  • Andrzej Zbrzezny
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7784)


We consider multi-agent systems’ (MASs) modelled by deontic interleaved interpreted systems and we provide a new SAT-based bounded model checking (BMC) method for these systems. The properties of MASs are expressed by means of the metric temporal logic with discrete semantics and extended to include epistemic and deontic operators. The proposed BMC approach is based on the state of the art solutions to BMC. We test our results on a typical MASs scenario: train controller problem with faults.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abdulla, P.A., Bjesse, P., Eén, N.: Symbolic Reachability Analysis Based on SAT-Solvers. In: Graf, S. (ed.) TACAS 2000. LNCS, vol. 1785, pp. 411–425. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. 2.
    Alur, R., Henzinger, T.A.: Logics and Models of Real Time: A Survey. In: Huizing, C., de Bakker, J.W., Rozenberg, G., de Roever, W.-P. (eds.) REX 1991. LNCS, vol. 600, pp. 74–106. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  3. 3.
    Aqvist, L.: Deontic logic. In: Handbook of Philosophical Logic. Extensions of Classical Logic, vol. II, pp. 605–714. Reidel, Dordrecht (1984)CrossRefGoogle Scholar
  4. 4.
    Biere, A., Heljanko, K., Junttila, T., Latvala, T., Schuppan, V.: Linear encodings of bounded LTL model checking. Logical Methods in Computer Science 2(5:5), 1–64 (2006)MathSciNetGoogle Scholar
  5. 5.
    Cabodi, G., Camurati, P., Quer, S.: Can BDD compete with SAT solvers on bounded model checking? In: Proceedings of DAC 2002, pp. 117–122 (2002)Google Scholar
  6. 6.
    Clarke, E.M., Allen Emerson, E.: Design and Synthesis of Synchronization Skeletons for Branching-Time Temporal Logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982)CrossRefGoogle Scholar
  7. 7.
    Clarke, E., Grumberg, O., Hamaguchi, K.: Another Look at LTL Model Checking. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 415–427. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  8. 8.
    Sistla, A.P., Emerson, E.A., Mok, A.K., Srinivasan, J.: Quantitative temporal reasoning. Real-Time Systems 4(4), 331–352 (1992)CrossRefGoogle Scholar
  9. 9.
    Emerson, E.A.: Temporal and modal logic. In: Handbook of Theoretical Computer Science, vol. B, ch. 16, pp. 996–1071. Elsevier Science Publishers (1990)Google Scholar
  10. 10.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1995)zbMATHGoogle Scholar
  11. 11.
    Furia, C.A., Spoletini, P.: Tomorrow and All our Yesterdays: MTL Satisfiability over the Integers. In: Fitzgerald, J.S., Haxthausen, A.E., Yenigun, H. (eds.) ICTAC 2008. LNCS, vol. 5160, pp. 126–140. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Huang, X., Luo, C., van der Meyden, R.: Improved Bounded Model Checking for a Fair Branching-Time Temporal Epistemic Logic. In: van der Meyden, R., Smaus, J.-G. (eds.) MoChArt 2010. LNCS, vol. 6572, pp. 95–111. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  13. 13.
    Jones, A., Lomuscio, A.: A BDD-based BMC approach for the verification of multi-agent systems. In: Proceedings of CS&P 2009, vol. 1, pp. 253–264. Warsaw University (2009)Google Scholar
  14. 14.
    Kacprzak, M., Lomuscio, A., Łasica, T., Penczek, W., Szreter, M.: Verifying Multi-agent Systems via Unbounded Model Checking. In: Hinchey, M.G., Rash, J.L., Truszkowski, W.F., Rouff, C.A. (eds.) FAABS 2004. LNCS (LNAI), vol. 3228, pp. 189–212. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  15. 15.
    Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Systems 2(4), 255–299 (1990)CrossRefGoogle Scholar
  16. 16.
    Levesque, H.: A logic of implicit and explicit belief. In: Proceedings of the 6th National Conference of the AAAI, pp. 198–202. Morgan Kaufman (1984)Google Scholar
  17. 17.
    Lomuscio, A., Penczek, W., Qu, H.: Partial order reduction for model checking interleaved multi-agent systems. In: AAMAS, pp. 659–666. IFAAMAS Press (2010)Google Scholar
  18. 18.
    Lomuscio, A., Sergot, M.: Deontic interpreted systems. Studia Logica 75(1), 63–92 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Męski, A., Penczek, W., Szreter, M.: Bounded model checking linear time and knowledge using decision diagrams. In: Proceedings of CS&P 2011, pp. 363–375 (2011)Google Scholar
  20. 20.
    Męski, A., Penczek, W., Szreter, M.: BDD-based Bounded Model Checking for LTLK over Two Variants of Interpreted Systems. In: Proceedings of LAM 2012, pp. 35–50 (2012)Google Scholar
  21. 21.
    Męski, A., Penczek, W., Szreter, M., Woźna-Szcześniak, B., Zbrzezny, A.: Two Approaches to Bounded Model Checking for Linear Time Logic with Knowledge. In: Jezic, G., Kusek, M., Nguyen, N.-T., Howlett, R.J., Jain, L.C. (eds.) KES-AMSTA 2012. LNCS, vol. 7327, pp. 514–523. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  22. 22.
    Penczek, W., Lomuscio, A.: Verifying epistemic properties of multi-agent systems via bounded model checking. In: Proceedings of AAMAS 2003, pp. 209–216. ACM (2003)Google Scholar
  23. 23.
    Penczek, W., Woźna-Szcześniak, B., Zbrzezny, A.: Towards SAT-based BMC for LTLK over interleaved interpreted systems. Fundamenta Informaticae 119(3-4), 373–392 (2012)zbMATHGoogle Scholar
  24. 24.
    Quielle, J.P., Sifakis, J.: Specification and Verification of Concurrent Systems in CESAR. In: Dezani-Ciancaglini, M., Montanari, U. (eds.) Programming 1982. LNCS, vol. 137, pp. 337–351. Springer, Heidelberg (1982)CrossRefGoogle Scholar
  25. 25.
    Raimondi, F., Lomuscio, A.: Automatic Verification of Deontic Properties of Multi-agent Systems. In: Lomuscio, A., Nute, D. (eds.) DEON 2004. LNCS (LNAI), vol. 3065, pp. 228–242. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  26. 26.
    Raimondi, F., Lomuscio, A.: Automatic verification of multi-agent systems by model checking via OBDDs. Journal of Applied Logic 5(2), 235–251 (2005)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Wooldridge, M.: An introduction to multi-agent systems. John Wiley, England (2002)Google Scholar
  28. 28.
    Woźna, B.: Bounded Model Checking for the universal fragment of CTL*. Fundamenta Informaticae 63(1), 65–87 (2004)MathSciNetzbMATHGoogle Scholar
  29. 29.
    Woźna, B., Lomuscio, A., Penczek, W.: Bounded model checking for deontic interpreted systems. In: Proceedings of LCMAS 2004. ENTCS, vol. 126, pp. 93–114. Elsevier (2005)Google Scholar
  30. 30.
    Woźna-Szcześniak, B., Zbrzezny, A.: SAT-Based Bounded Model Checking for Deontic Interleaved Interpreted Systems. In: Jezic, G., Kusek, M., Nguyen, N.-T., Howlett, R.J., Jain, L.C. (eds.) KES-AMSTA 2012. LNCS, vol. 7327, pp. 494–503. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  31. 31.
    Woźna-Szcześniak, B., Zbrzezny, A., Zbrzezny, A.: The BMC Method for the Existential Part of RTCTLK and Interleaved Interpreted Systems. In: Antunes, L., Pinto, H.S. (eds.) EPIA 2011. LNCS, vol. 7026, pp. 551–565. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  32. 32.
    Zbrzezny, A.: Improving the translation from ECTL to SAT. Fundamenta Informaticae 85(1-4), 513–531 (2008)MathSciNetzbMATHGoogle Scholar
  33. 33.
    Zbrzezny, A.: A new translation from ECTL* to SAT. Fundamenta Informaticae 120(3-4), 377–397 (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Bożena Woźna-Szcześniak
    • 1
  • Andrzej Zbrzezny
    • 1
  1. 1.IMCSJan Długosz UniversityCzȩstochowaPoland

Personalised recommendations