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A Temporal Logic of Robustness

  • Tim French
  • John C. Mc Cabe-Dansted
  • Mark Reynolds
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

RoCTL* Decidability Modal Logic Robustness Branching Time Logic QCTL* 

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References

  1. 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. 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. 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. 4.
    Forrester, J.W.: Gentle murder, or the adverbial samaritan. J. Philos. 81(4), 193–197 (1984)CrossRefMathSciNetGoogle Scholar
  5. 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. 6.
    McCarty, L.T.: Defeasible deontic reasoning. Fundam. Inform. 21(1/2), 125–148 (1994)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Belnap, N.: Backwards and forwards in the modal logic of agency. Philos. Phenomen. Res. 51(4), 777–807 (1991)CrossRefGoogle Scholar
  8. 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)zbMATHGoogle Scholar
  9. 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. 10.
    Long, W., Sato, Y., Horigome, M.: Quantification of sequential failure logic for fault tree analysis. Reliab. Eng. Syst. Safe. 67, 269–274 (2000)CrossRefGoogle Scholar
  11. 11.
    Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Form. Asp. Comput. 6(5), 512–535 (1994)zbMATHCrossRefGoogle Scholar
  12. 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. 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. 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. 15.
    Arnold, A., Vincent, A., Walukiewicz, I.: Games for synthesis of controllers with partial observation. TCS 303(1), 7–34 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Reynolds, M.: An axiomatization of full computation tree logic. J. Symb. Log. 66(3), 1011–1057 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Emerson, E.A.: Alternative semantics for temporal logics. TCS 26, 121–130 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  18. 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. 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)CrossRefGoogle Scholar
  20. 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. 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)zbMATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    French, T.: Bisimulation Quantifiers for Modal Logics. PhD thesis, UWA (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Tim French
    • 1
  • John C. Mc Cabe-Dansted
    • 1
  • Mark Reynolds
    • 1
  1. 1.University of Western Australia, Department of Computer Science and Software Engineering 

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