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Reasoning about Time-Dependent Multi-agents: Foundations of Theorem Proving and Model Checking

  • Norihiro Kamide
Chapter
  • 351 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7190)

Abstract

Firstly, an extension of linear-time temporal logic (LTL), called an agents-indexed linear-time temporal logic (ALTL), is introduced as a Gentzen-type sequent calculus. ALTL is intended to appropriately express reasoning about time-dependent multi-agents within a proof system. The cut-elimination and completeness theorems for ALTL are shown. Secondly, an extension of computation tree logic (CTL), called an agents-indexed computation tree logic (ACTL), is introduced as a Kripke-type semantics. ACTL is intended to appropriately formalize reasoning about time-dependent multi-agents within an executable temporal logic by model checking. The model-checking, validity and satisfiability problems for ACTL are shown to be decidable.

Keywords

Agents-indexed linear-time temporal logic agents-indexed computation tree logic time-dependent multi-agent sequent calculus model checking completeness theorem 

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References

  1. 1.
    Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. Journal of the ACM 49(5), 672–713 (2002)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Clarke, E.M., Emerson, E.A.: Design and Synthesis of Synchronization Skeletons using Branching Time Temporal Logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982)CrossRefGoogle Scholar
  3. 3.
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model checking. The MIT Press (1999)Google Scholar
  4. 4.
    Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, Formal Models and Semantics (B), pp. 995–1072. Elsevier, MIT Press (1990)Google Scholar
  5. 5.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about knowledge. MIT Press (1995)Google Scholar
  6. 6.
    Gammie, P., van der Meyden, R.: MCK: Model Checking the Logic of Knowledge. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 479–483. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Kacprzak, M., Nabialek, W., Niewiadomski, A., Penczek, W., Polroa, A., Szreter, M., Wozawa, B., Zbrzezny, A.: VerICS 2007: A model checker for real-time and multi-agent systems. Fundamenta Informaticae 85(1-4), 313–328 (2008)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Kamide, N.: Embedding Linear-Time Temporal Logic into Infinitary Logic: Application to Cut-Elimination for Multi-agent Infinitary Epistemic Linear-Time Temporal Logic. In: Fisher, M., Sadri, F., Thielscher, M. (eds.) CLIMA IX. LNCS (LNAI), vol. 5405, pp. 57–76. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Kamide, N.: A Proof System for Time-dependent Multi-agents. In: Setchi, R., Jordanov, I., Howlett, R.J., Jain, L.C. (eds.) KES 2010. LNCS (LNAI), vol. 6276, pp. 178–187. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Kamide, N., Wansing, H.: Combining linear-time temporal logic with constructiveness and paraconsistency. Journal of Applied Logic 8, 33–61 (2010)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Kawai, H.: Sequential calculus for a first order infinitary temporal logic. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 33, 423–432 (1987)zbMATHCrossRefGoogle Scholar
  12. 12.
    Konikowska, B., Penczek, W.: Model checking for multi-valued computation tree logics. In: Fitting, M., Ołowska, E. (eds.) Beyond Two: Theory and Applications of Multiple Valued Logic, pp. 193–210. Physica-Verlag (2003)Google Scholar
  13. 13.
    Konikowska, B., Penczek, W.: Model checking for multivalued logic knowledge and time. In: Proceedings of the 5th International Conference on Autonomous Agent and Multiagent Systems (AAMAS 2006), pp. 169–176. ACM (2006)Google Scholar
  14. 14.
    Kozen, D.: Results on the propositional mu-calculus. Theoretical Computer Science 27, 333–354 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Lewis, D.K.: Convention: A philosophical study. Harvard University Press (1969)Google Scholar
  16. 16.
    Lomuscio, A., Raimondi, F.: mcmas: A Model Checker for Multi-agent Systems. In: Hermanns, H. (ed.) TACAS 2006. LNCS, vol. 3920, pp. 450–454. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Pnueli, A.: The temporal logic of programs. In: Proceedings of the 18th IEEE Symposium on Foundations of Computer Science, pp. 46–57 (1977)Google Scholar
  18. 18.
    van der Hoek, W., Wooldridge, M.: Cooperation, knowledge, and time: Alternating-time temporal epistemic logic and its applications. Studia Logica 75(1), 125–157 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    van der Meyden, R., Shilov, N.V.: Model Checking Knowledge and Time in Systems with Perfect Recall (Extended Abstract). In: Pandu Rangan, C., Raman, V., Sarukkai, S. (eds.) FST TCS 1999. LNCS, vol. 1738, pp. 432–445. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  20. 20.
    van der Meyden, R., Wong, K.-S.: Complete axiomatizations for reasoning about knowledge and branching time. Studia Logica 75(1), 93–123 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Wooldridge, M.: An introduction to multiagent systems. John Wiley and Sons Ltd. (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Norihiro Kamide
    • 1
  1. 1.Waseda Institute for Advanced StudyWaseda UniversityTokyoJapan

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