Skip to main content

A Temporal Logic of Robustness

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4720))

Abstract

It can be desirable to specify polices that require a system to achieve some outcome even if a certain number of failures occur. This paper proposes a logic, RoCTL*, which extends CTL* with operators from Deontic logic, and a novel operator referred to as “Robustly”. This novel operator acts as variety of path quantifier allowing us to consider paths which deviate from the desired behaviour of the system. Unlike most path quantifiers, the Robustly operator must be evaluated over a path rather than just a state; the Robustly operator quantifies over paths produced from the current path by altering a single step. The Robustly operator roughly represents the phrase “even if an additional failure occurs now or in the future”. This paper examines the expressivity of this new logic, motivates its use and shows that it is decidable.

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

Buying options

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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Emerson, E.A., Sistla, A.P.: Deciding full branching time logic. Technical report, University of Texas at Austin, Austin, TX, USA (1985)

    Google Scholar 

  2. Clarke, E., Emerson, E.: Synthesis of synchronization skeletons for branching time temporal logic. In: Proc. IBM Workshop on Log. of Progr., Yorktown Heights, pp. 52–71. Springer, Heidelberg (1981)

    Google Scholar 

  3. French, T., McCabe-Dansted, J.C., Reynolds, M.: A temporal logic of robustness, RoCTL*. Technical report, UWA (2007) http://dansted.org/RoCTL07.pdf

  4. Forrester, J.W.: Gentle murder, or the adverbial samaritan. J. Philos. 81(4), 193–197 (1984)

    Article  MathSciNet  Google Scholar 

  5. van der Torre, L.W.N., Tan, Y.: The temporal analysis of Chisholm’s paradox. In: Senator, T., Buchanan, B. (eds.) Proc. 14th Nation. Conf. on AI and 9th Innov. Applic. of AI Conf., Menlo Park, California, pp. 650–655. AAAI Press, Stanford, California (1998)

    Google Scholar 

  6. McCarty, L.T.: Defeasible deontic reasoning. Fundam. Inform. 21(1/2), 125–148 (1994)

    MATH  MathSciNet  Google Scholar 

  7. Belnap, N.: Backwards and forwards in the modal logic of agency. Philos. Phenomen. Res. 51(4), 777–807 (1991)

    Article  Google Scholar 

  8. de Weerdt, M., Bos, A., Tonino, H., Witteveen, C.: A resource logic for multi-agent plan merging. Annals of Math. and AI 37(1-2), 93–130 (2003)

    MATH  Google Scholar 

  9. Broersen, J., Dignum, F., Dignum, V., Meyer, J.J.C.: In: Designing a Deontic Logic of Deadlines. In: Lomuscio, A.R., Nute, D. (eds.) DEON 2004. LNCS (LNAI), vol. 3065, pp. 43–56. Springer, Heidelberg (2004)

    Google Scholar 

  10. Long, W., Sato, Y., Horigome, M.: Quantification of sequential failure logic for fault tree analysis. Reliab. Eng. Syst. Safe. 67, 269–274 (2000)

    Article  Google Scholar 

  11. Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Form. Asp. Comput. 6(5), 512–535 (1994)

    Article  MATH  Google Scholar 

  12. Aldewereld, H., Grossi, D., Vazquez-Salceda, J., Dignum, F.: Designing normative behaviour by the use of landmarks. In: Agents, Norms and Institutions for Regulated Multiag. Syst., Utrecht, The Netherlands (2005)

    Google Scholar 

  13. Rodrigo, A., Eduardo, A.: Normative pragmatics for agent communication languages. In: Akoka, J., Liddle, S.W., Song, I.-Y., Bertolotto, M., Comyn-Wattiau, I., van den Heuvel, W.-J., Kolp, M., Trujillo, J., Kop, C., Mayr, H.C. (eds.) Perspectives in Conceptual Modeling. LNCS, vol. 3770, pp. 172–181. Springer, Heidelberg (2005)

    Google Scholar 

  14. Jéron, T., Marchand, H., Pinchinat, S., Cordier, M.O.: Supervision patterns in discrete event systems diagnosis. In: 8th Internat. Workshop on Discrete Event Syst., pp. 262–268 (2006)

    Google Scholar 

  15. Arnold, A., Vincent, A., Walukiewicz, I.: Games for synthesis of controllers with partial observation. TCS 303(1), 7–34 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  16. Reynolds, M.: An axiomatization of full computation tree logic. J. Symb. Log. 66(3), 1011–1057 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  17. Emerson, E.A.: Alternative semantics for temporal logics. TCS 26, 121–130 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  18. Kupferman, O.: Augmenting branching temporal logics with existential quantification over atomic propositions. In: Comput. Aid. Verfic., Proc. 7th Int. Conf., Liege, pp. 325–338. Springer, Heidelberg (1995)

    Google Scholar 

  19. Emerson, E.A., Sistla, A.P.: Deciding branching time logic. In: STOC 1984: Proc. 16th annual ACM sympos. on Theory of computing, New York, NY, USA, pp. 14–24. ACM Press, New York (1984)

    Chapter  Google Scholar 

  20. French, T.: Decidability of quantifed propositional branching time logics. In: AI 2001. Proc. 14th Austral. Joint Conf. on AI, London, UK, pp. 165–176. Springer, Heidelberg (2001)

    Google Scholar 

  21. Sistla, A.P., Vardi, M.Y., Wolper, P.: The complementation problem for buc̈hi automata with applications to temporal logic. TCS 49(2-3), 217–237 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  22. French, T.: Bisimulation Quantifiers for Modal Logics. PhD thesis, UWA (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Boris Konev Frank Wolter

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

French, T., Mc Cabe-Dansted, J.C., Reynolds, M. (2007). A Temporal Logic of Robustness. In: Konev, B., Wolter, F. (eds) Frontiers of Combining Systems. FroCoS 2007. Lecture Notes in Computer Science(), vol 4720. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74621-8_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-74621-8_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74620-1

  • Online ISBN: 978-3-540-74621-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics