Skip to main content

Model Checking Propositional Deontic Temporal Logic via a μ-Calculus Characterization

  • Conference paper

Part of the Lecture Notes in Computer Science book series (LNPSE,volume 7498)

Abstract

In this paper, we present a characterization of a propositional deontic temporal logic into μ-calculus. This logic has been proposed to specify and reason about fault tolerant systems, and even though is known to be decidable, no tool realizing its corresponding decision procedure has been developed. A main motivation for our work is enabling for the use of model checking, for analyzing specifications in this deontic temporal logic.

We present the technical details involved in the characterization, and prove that the model checking problem on the deontic temporal logic is correctly reduced to μ-calculus model checking. We also show that counterexamples are preserved, which is crucial for our model checking purposes. Finally, we illustrate our approach via a case study, including the verification of some properties using a μ-calculus model checker.

Keywords

  • Model Check
  • Fault Tolerance
  • Decision Procedure
  • Parallel Execution
  • Deontic 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.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   72.00
Price excludes VAT (Canada)
  • 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bernardeschi, C., Fantechi, A., Gnesi, S.: Model checking fault tolerant systems. Softw. Test., Verif. Reliab. 12(4), 251–275 (2002)

    CrossRef  Google Scholar 

  2. Biere, A.: μcke - Efficient μ-Calculus Model Checking. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 468–471. Springer, Heidelberg (1997)

    CrossRef  Google Scholar 

  3. Castro, P.F.: Deontic Action Logics for the Specification and Analysis of Fault-Tolerance. PhD thesis, McMaster University, Department of Computing and Software (2009)

    Google Scholar 

  4. Castro, P.F., Maibaum, T.S.E.: A Tableaux System for Deontic Action Logic. In: van der Meyden, R., van der Torre, L. (eds.) DEON 2008. LNCS (LNAI), vol. 5076, pp. 34–48. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  5. Castro, P.F., Maibaum, T.S.E.: Deontic action logic, atomic boolean algebra and fault-tolerance. Journal of Applied Logic 7(4), 441–466 (2009)

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Coenen, J.: Formalisms for Program Reification and Fault Tolerance. PhD thesis, Tenische Universiteit Eindhoven (1994)

    Google Scholar 

  7. Cristian, F.: A rigorous approach to fault-tolerant programming. IEEE Trans. Software Eng. 11, 23–31 (1985)

    CrossRef  Google Scholar 

  8. French, T., Mc Cabe-Dansted, J.C., Reynolds, M.: A Temporal Logic of Robustness. In: Konev, B., Wolter, F. (eds.) FroCos 2007. LNCS (LNAI), vol. 4720, pp. 193–205. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  9. Gärtner, F.: Specification for fault-tolerance: A comedy of failures. Technical report, Darmstadt University of Technology (1998)

    Google Scholar 

  10. Goguen, J.A., Burstall, R.M.: Institutions: Abstract model theory for specification and programming. Journal of the Association of Computing Machinery (1992)

    Google Scholar 

  11. Goguen, J.A., Rosu, G.: Institution morphisms. Formal Asp. Comput. 13(3-5), 274–307 (2002)

    CrossRef  MATH  Google Scholar 

  12. Janowski, T.: On Bisimulation, Fault-Monotonicity and Provable Fault-tolerance. In: Johnson, M. (ed.) AMAST 1997. LNCS, vol. 1349, pp. 292–306. Springer, Heidelberg (1997)

    CrossRef  Google Scholar 

  13. Lamport, L., Merz, S.: Specifying and Verifying Fault-Tolerant Systems. In: Langmaack, H., de Roever, W.-P., Vytopil, J. (eds.) FTRTFT 1994 and ProCoS 1994. LNCS, vol. 863, pp. 41–76. Springer, Heidelberg (1994)

    CrossRef  Google Scholar 

  14. Laranjeira, L.A., Malek, M., Jenevein, R.M.: Nest: A nested-predicate scheme for fault tolerance. IEEE Trans. Computers 42, 1303–1324 (1993)

    CrossRef  Google Scholar 

  15. Liu, Z., Joseph, M.: Specification and verification of fault-tolerance, timing, and scheduling. ACM Trans. Program. Lang. Syst. 21(1), 46–89 (1999)

    CrossRef  Google Scholar 

  16. Lomuscio, A., Sergot, M.J.: A formalisation of violation, error recovery, and enforcement in the bit transmission problem. Journal of Applied Logic 2, 93–116 (2004)

    CrossRef  MathSciNet  MATH  Google Scholar 

  17. Magee, J., Maibaum, T.S.E.: Towards specification, modelling and analysis of fault tolerance in self managed systems. In: Proceeding of the 2006 International Workshop on Self-Adaptation and Self-Managing Systems (2006)

    Google Scholar 

  18. Schneider, F., Easterbrook, S.M., Callahan, J.R., Holzmann, G.J.: Validating requirements for fault tolerant systems using model checking. In: 3rd International Conference on Requirements Engineering, ICRE 1998 (1998)

    Google Scholar 

  19. Schneider, K.: Verification of Reactive Systems, Formal Methods and Algorithms. Springer (2004)

    Google Scholar 

  20. Yokogawa, T., Tsuchiya, T., Kikuno, T.: Automatic verification of fault tolerance using model checking. In: Pacific Rim International Symposium on Dependable Computing (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Acosta, A., Kilmurray, C., Castro, P.F., Aguirre, N.M. (2012). Model Checking Propositional Deontic Temporal Logic via a μ-Calculus Characterization. In: Gheyi, R., Naumann, D. (eds) Formal Methods: Foundations and Applications. SBMF 2012. Lecture Notes in Computer Science, vol 7498. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33296-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33296-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33295-1

  • Online ISBN: 978-3-642-33296-8

  • eBook Packages: Computer ScienceComputer Science (R0)