Skip to main content

Imperfect Information in Alternating-Time Temporal Logic on Finite Traces

  • 635 Accesses

Part of the Lecture Notes in Computer Science book series (LNAI,volume 11873)

Abstract

We introduce a logic to reason about strategic abilities in finite games under imperfect information. We interpret Alternating-time Temporal Logic on interpreted systems with final states, where agents only have partial observability of the system’s global state. We consider the model checking problem in this setting. We prove that the complexity results available for the case of infinite traces carry over to the finite traces case. We show that when only public actions are allowed, the verification problem under perfect recall becomes decidable.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-030-33792-6_31
  • Chapter length: 9 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   109.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-33792-6
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   139.99
Price excludes VAT (USA)

References

  1. Alur, R., Henzinger, T., Kupferman, O.: Alternating-time temporal logic. J. ACM 49(5), 672–713 (2002)

    MathSciNet  CrossRef  Google Scholar 

  2. Bacchus, F., Kabanza, F.: Using temporal logics to express search control knowledge for planning. Art. Int. 116(1–2), 123–191 (2000)

    MathSciNet  CrossRef  Google Scholar 

  3. Baier, J.A., McIlraith, S.A.: Planning with first-order temporally extended goals using heuristic search. In: AAAI, pp. 788–795 (2006)

    Google Scholar 

  4. Belardinelli, F., Lomuscio, A., Murano, A., Rubin, S.: Verification of multi-agent systems with imperfect information and public actions. In: AAMAS, pp. 1268–1276 (2017)

    Google Scholar 

  5. Belardinelli, F., Lomuscio, A., Murano, A., Rubin, S.: Alternating-time temporal logic on finite traces. In: IJCAI, pp. 77–83 (2018). https://doi.org/10.24963/ijcai.2017/14

  6. Belardinelli, F., Lomuscio, A., Murano, A., Rubin, S.: Decidable verification of multi-agent systems with bounded private actions. In: AAMAS, pp. 1865–1867 (2018)

    Google Scholar 

  7. Camacho, A., Triantafillou, E., Muise, C., Baier, J., McIlraith, S.: Non-deterministic planning with temporally extended goals: LTL over finite and infinite traces. In: AAAI, pp. 3716–3724 (2017)

    Google Scholar 

  8. De Giacomo, G., De Masellis, R., Grasso, M., Maggi, F.M., Montali, M.: Monitoring business metaconstraints based on LTL and LDL for finite traces. In: Sadiq, S., Soffer, P., Völzer, H. (eds.) BPM 2014. LNCS, vol. 8659, pp. 1–17. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10172-9_1

    CrossRef  Google Scholar 

  9. De Giacomo, G., De Masellis, R., Montali, M.: Reasoning on LTL on finite traces: insensitivity to infiniteness. In: AAAI, pp. 1027–1033 (2014)

    Google Scholar 

  10. De Giacomo, G., Vardi, M.Y.: Synthesis for LTL and LDL on finite traces. In: IJCAI, pp. 1558–1564 (2015)

    Google Scholar 

  11. De Giacomo, G., Vardi, M.: Linear temporal logic and linear dynamic logic on finite traces. In: IJCAI, pp. 854–860 (2013)

    Google Scholar 

  12. Dima, C., Tiplea, F.: Model-checking ATL under imperfect information and perfect recall semantics is undecidable. CoRR abs/1102.4225 (2011). http://arxiv.org/abs/1102.4225

  13. Emerson, E.A., Halpern, J.Y.: “sometimes” and “not never” revisited: on branching versus linear time temporal logic. J. ACM 33(1), 151–178 (1986)

    MathSciNet  CrossRef  Google Scholar 

  14. Emerson, E., Jutla, C., Sistla, A.: On model checking for the \(\mu \)-calculus and its fragments. Theor. Comp. Sci. 258(1–2), 491–522 (2001)

    Google Scholar 

  15. Fagin, R., Halpern, J., Moses, Y., Vardi, M.: Reasoning About Knowledge. MIT, Cambridge (1995)

    MATH  Google Scholar 

  16. Filiot, E., Jin, N., Raskin, J.: Antichains and compositional algorithms for LTL synthesis. Formal Methods Syst. Des. 39(3), 261–296 (2011)

    CrossRef  Google Scholar 

  17. Gerevini, A., Haslum, P., Long, D., Saetti, A., Dimopoulos, Y.: Deterministic planning in the fifth international planning competition: PDDL3 and experimental evaluation of the planners. Artif. Intell. 173(5–6), 619–668 (2009). https://doi.org/10.1016/j.artint.2008.10.012

    MathSciNet  CrossRef  MATH  Google Scholar 

  18. Gutierrez, J., Perelli, G., Wooldridge, M.: Iterated games with LDL goals over finite traces. In: AAMAS, pp. 696–704 (2017)

    Google Scholar 

  19. Jamroga, W., van der Hoek, W.: Agents that know how to play. Fund. Inf. 62, 1–35 (2004)

    MathSciNet  MATH  Google Scholar 

  20. Kominis, F., Geffner, H.: Multiagent online planning with nested beliefs and dialogue. In: ICAPS, pp. 186–194 (2017)

    Google Scholar 

  21. Kong, J., Lomuscio, A.: Model checking multi-agent systems against LDLK specifications on finite traces. In: AAMAS, pp. 166–174 (2018)

    Google Scholar 

  22. Kupferman, O., Piterman, N., Vardi, M.: Safraless compositional synthesis. In: CAV, pp. 31–44 (2006)

    Google Scholar 

  23. Montali, M., Pesic, M., van der Aalst, W., Chesani, F., Mello, P., Storari, S.: Declarative specification and verification of service choreographiess. ACM Trans. Web (TWEB) 4(1), 3 (2010)

    Google Scholar 

  24. Pesic, M., Bosnacki, D., van der Aalst, W.: Enacting declarative languages using LTL: avoiding errors and improving performance. In: SPIN, pp. 146–161 (2010)

    Google Scholar 

  25. Pesic, M., van der Aalst, W.M.P.: A declarative approach for flexible business processes management. In: Eder, J., Dustdar, S. (eds.) BPM 2006. LNCS, vol. 4103, pp. 169–180. Springer, Heidelberg (2006). https://doi.org/10.1007/11837862_18

    CrossRef  Google Scholar 

  26. Tsai, M.H., Fogarty, S., Vardi, M., Tsay, Y.K.: State of Büchi complementation. LMCS 10, 4 (2014). https://doi.org/10.2168/LMCS-10(4:13)2014

    CrossRef  MATH  Google Scholar 

  27. Vardi, M.Y., Stockmeyer, L.: Improved upper and lower bounds for modal logics of programs. In: STOC, pp. 240–251 (1985)

    Google Scholar 

Download references

Acknowledgements

The authors acknowledge support of ANR JCJC Project SVeDaS (ANR-16-CE40-0021). Alessio Lomuscio is supported by a Royal Academy Chair in Emerging Technologies.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Francesco Belardinelli .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Verify currency and authenticity via CrossMark

Cite this paper

Belardinelli, F., Lomuscio, A., Murano, A., Rubin, S. (2019). Imperfect Information in Alternating-Time Temporal Logic on Finite Traces. In: Baldoni, M., Dastani, M., Liao, B., Sakurai, Y., Zalila Wenkstern, R. (eds) PRIMA 2019: Principles and Practice of Multi-Agent Systems. PRIMA 2019. Lecture Notes in Computer Science(), vol 11873. Springer, Cham. https://doi.org/10.1007/978-3-030-33792-6_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-33792-6_31

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33791-9

  • Online ISBN: 978-3-030-33792-6

  • eBook Packages: Computer ScienceComputer Science (R0)