Skip to main content

On Satisfiability in ATL with Strategy Contexts

  • Conference paper
Logics in Artificial Intelligence (JELIA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7519))

Included in the following conference series:

Abstract

This paper is a study of Brihaye et al.’s ATL with strategy contexts. We focus on memory-less strategies and establish that the resulting logic is undecidable. An immediate corollary follows that the problem of satisfiability checking of every variant of ATL with strategy context introduced by Brihaye et al. is undecidable. We also relate ATL\(_{\textit{sc}}\) with memory-less strategies with ATL with explicit strategies, providing a decidable fragment.

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

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ågotnes, T., Goranko, V., Jamroga, W.: Alternating-time temporal logics with irrevocable strategies. In: Proceedings of TARK 2007, pp. 15–24. ACM (2007)

    Google Scholar 

  2. Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. The Journal of the ACM 49(5), 672–713 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  3. Börger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem. In: Perspectives Mathematical Logic. Springer (1997)

    Google Scholar 

  4. Brihaye, T., Da Costa, A., Laroussinie, F., Markey, N.: ATL with Strategy Contexts and Bounded Memory. In: Artemov, S., Nerode, A. (eds.) LFCS 2009. LNCS, vol. 5407, pp. 92–106. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Broersen, J., Herzig, A., Troquard, N.: A STIT-Extension of ATL. In: Fisher, M., van der Hoek, W., Konev, B., Lisitsa, A. (eds.) JELIA 2006. LNCS (LNAI), vol. 4160, pp. 69–81. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  6. Da Costa, A., Laroussinie, F., Markey, N.: ATL with strategy contexts: Expressiveness and model checking. In: Proceedings of FSTTCS 2010. LIPIcs, vol. 8, pp. 120–132. Schloss Dagstuhl – Leibniz-Zentrum fuer Informatik (2010)

    Google Scholar 

  7. Gabbay, D., Kurucz, A., Wolter, F., Zakharyaschev, M.: Many-dimensional modal logics: theory and applications. Studies in Logic, vol. 148. Elsevier Science (2003)

    Google Scholar 

  8. Gurevich, Y., Lewis, H.R.: The word problem for cancellation semigroups with zero. The Journal of Symbolic Logic 49(1), 184–191 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  9. Halmos, P.: Algebraic logic, IV. Transactions of the AMS 86, 1–27 (1957)

    Google Scholar 

  10. Herzig, A., Schwarzentruber, F.: Properties of logics of individual and group agency. In: Proceedings of AiML 2008, pp. 133–149. College Publications (2008)

    Google Scholar 

  11. Horty, J.F.: Agency and Deontic Logic. Oxford University Press, Oxford (2001)

    Book  MATH  Google Scholar 

  12. Johnson, J.: Nonfinitizability of classes of representable polyadic algebras. The Journal of Symbolic Logic 34(3), 344–352 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kurucz, A.: S5 x S5 x S5 lacks the finite model property. In: Proceedings of AiML 2002, pp. 321–327. World Scientific (2002)

    Google Scholar 

  14. Laroussinie, F., Markey, N., Oreiby, G.: On the expressiveness and complexity of ATL. Logical Methods in Computer Science 4(2) (2008)

    Google Scholar 

  15. Maddux, R.: The equational theory of CA3 is undecidable. The Journal of Symbolic Logic 45(2), 311–316 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  16. Marx, M.: Complexity of products of modal logics. Journal of Logic and Computation 9(2), 197–214 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  17. Mortimer, M.: On languages with two variables. Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 21, 135–140 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  18. Troquard, N., Walther, D.: ATL with contexts: agency and explicit strategies. In: Proceedings of LAMAS@AAMAS 2012 (2012)

    Google Scholar 

  19. Walther, D., van der Hoek, W., Wooldridge, M.: Alternating-time temporal logic with explicit strategies. In: Proceedings of TARK 2007, pp. 269–278. ACM (2007)

    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

Troquard, N., Walther, D. (2012). On Satisfiability in ATL with Strategy Contexts. In: del Cerro, L.F., Herzig, A., Mengin, J. (eds) Logics in Artificial Intelligence. JELIA 2012. Lecture Notes in Computer Science(), vol 7519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33353-8_31

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33353-8_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33352-1

  • Online ISBN: 978-3-642-33353-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics