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A Behavioral Hierarchy of Strategy Logic

  • Fabio Mogavero
  • Aniello Murano
  • Luigi Sauro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8624)

Abstract

Starting from the seminal work introducing Alternating Temporal Logic, formalisms for strategic reasoning have assumed a prominent role in multi-agent systems verification. Among the others, Strategy Logic (SL) allows to represent sophisticated solution concepts, by treating agent strategies as first-order objects.

A drawback from the high power of SL is to admit non-behavioral strategies: a choice of an agent, at a given point of a play, may depend on choices other agents can make in the future or in counterfactual plays. As the latter moves are unpredictable, such strategies cannot be easily implemented, making the use of the logic problematic in practice.

In this paper, we describe a hierarchy of SL fragments as syntactic restrictions of the recently defined Boolean-Goal Strategy Logic (SL[bg]). Specifically, we introduce Alternating-Goal Strategy Logic (SL[ag]) that, by imposing a suitable alternation over the nesting of the Boolean connectives in (SL[bg]), induces two dual chains of sets of formulas, the conjunctive and disjunctive ones. A formula belongs to the level i of the conjunctive chain if it just contains conjunctions of atomic goals together with a unique formula belonging to the disjunctive chain of level i − 1. The disjunctive chain is defined similarly. We formally prove that classic and behavioral semantics for (SL[ag]) coincide. Additionally, we study the related model-checking problem showing that it is 2ExpTime-complete.

Keywords

Model Check Multiagent System Atomic Proposition Strategy Logic Strategic Reasoning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Ågotnes, T., Goranko, V., Jamroga, W.: Alternating-Time Temporal Logics with Irrevocable Strategies. In: TARK 2007, pp. 15–24 (2007)Google Scholar
  2. 2.
    Ågotnes, T., Walther, D.: A Logic of Strategic Ability Under Bounded Memory. JLLI 18(1), 55–77 (2009)CrossRefzbMATHGoogle Scholar
  3. 3.
    Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-Time Temporal Logic. JACM 49(5), 672–713 (2002)CrossRefMathSciNetGoogle Scholar
  4. 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 (2009)CrossRefGoogle Scholar
  5. 5.
    Čermák, P., Lomuscio, A., Mogavero, F., Murano, A.: MCMAS-SLK: A Model Checker for the Verification of Strategy Logic Specifications. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 525–532. Springer, Heidelberg (2014)Google Scholar
  6. 6.
    Chatterjee, K., Henzinger, T.A., Piterman, N.: Strategy Logic. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 59–73. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  7. 7.
    Chatterjee, K., Henzinger, T.A., Piterman, N.: Strategy Logic. IC 208(6), 677–693 (2010)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Emerson, E.A., Halpern, J.Y.: “Sometimes” and “Not Never” Revisited: On Branching Versus Linear Time. JACM 33(1), 151–178 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Finkbeiner, B., Schewe, S.: Coordination Logic. In: Dawar, A., Veith, H. (eds.) CSL 2010. LNCS, vol. 6247, pp. 305–319. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Fisman, D., Kupferman, O., Lustig, Y.: Rational Synthesis. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 190–204. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Jamroga, W., Murano, A.: On Module Checking and Strategies. In: AAMAS 2014, pp. 701–708. International Foundation for Autonomous Agents and Multiagent Systems (2014)Google Scholar
  12. 12.
    Jamroga, W., Penczek, W.: Specification and Verification of Multi-Agent Systems. In: Bezhanishvili, N., Goranko, V. (eds.) ESSLLI 2010/2011. LNCS, vol. 7388, pp. 210–263. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  13. 13.
    Jamroga, W., van der Hoek, W.: Agents that Know How to Play. FI 63(2-3), 185–219 (2004)zbMATHGoogle Scholar
  14. 14.
    Kupferman, O., Vardi, M.Y., Wolper, P.: Module Checking. IC 164(2), 322–344 (2001)zbMATHMathSciNetGoogle Scholar
  15. 15.
    Lomuscio, A., Qu, H., Raimondi, F.: MCMAS: A Model Checker for the Verification of Multi-Agent Systems. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 682–688. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  16. 16.
    Lomuscio, A., Raimondi, F.: mcmas: A Model Checker for Multi-agent Systems. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 450–454. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Lomuscio, A., Raimondi, F.: Model Checking Knowledge, Strategies, and Games in Multi-Agent Systems. In: AAMAS 2006, pp. 161–168. International Foundation for Autonomous Agents and Multiagent Systems (2006)Google Scholar
  18. 18.
    Lopes, A.D.C., Laroussinie, F., Markey, N.: ATL with Strategy Contexts: Expressiveness and Model Checking. In: FSTTCS 2010. LIPIcs, vol. 8, pp. 120–132. Leibniz-Zentrum fuer Informatik (2010)Google Scholar
  19. 19.
    Mogavero, F., Murano, A., Perelli, G., Vardi, M.Y.: Reasoning About Strategies: On the Model-Checking Problem. Technical report, arXiv (2011)Google Scholar
  20. 20.
    Mogavero, F., Murano, A., Perelli, G., Vardi, M.Y.: What Makes Atl* Decidable? A Decidable Fragment of Strategy Logic. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 193–208. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  21. 21.
    Mogavero, F., Murano, A., Sauro, L.: On the Boundary of Behavioral Strategies. In: LICS 2013, pp. 263–272. IEEE Computer Society (2013)Google Scholar
  22. 22.
    Mogavero, F., Murano, A., Sauro, L.: Strategy Games: A Renewed Framework. In: AAMAS 2014, pp. 869–876. International Foundation for Autonomous Agents and Multiagent Systems (2014)Google Scholar
  23. 23.
    Mogavero, F., Murano, A., Vardi, M.Y.: Reasoning About Strategies. In: FSTTCS 2010. LIPIcs, vol. 8, pp. 133–144. Leibniz-Zentrum fuer Informatik (2010)Google Scholar
  24. 24.
    Mogavero, F., Murano, A., Vardi, M.Y.: Relentful Strategic Reasoning in Alternating-Time Temporal Logic. In: Clarke, E.M., Voronkov, A. (eds.) LPAR-16. LNCS (LNAI), vol. 6355, pp. 371–386. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  25. 25.
    Pinchinat, S.: A Generic Constructive Solution for Concurrent Games with Expressive Constraints on Strategies. In: Namjoshi, K.S., Yoneda, T., Higashino, T., Okamura, Y. (eds.) ATVA 2007. LNCS, vol. 4762, pp. 253–267. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  26. 26.
    Pnueli, A.: The Temporal Logic of Programs. In: FOCS 1977, pp. 46–57. IEEE Computer Society (1977)Google Scholar
  27. 27.
    Sauro, L., Villata, S.: Dependency in Cooperative Boolean Games. JLC 23(2), 425–444 (2013)zbMATHMathSciNetGoogle Scholar
  28. 28.
    Schewe, S.: ATL* Satisfiability is 2EXPTIME-Complete. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part II. LNCS, vol. 5126, pp. 373–385. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  29. 29.
    Schobbens, P.Y.: Alternating-Time Logic with Imperfect Recall 85(2), 82–93 (2004)Google Scholar
  30. 30.
    van der Hoek, W., Jamroga, W., Wooldridge, M.: A Logic for Strategic Reasoning. In: AAMAS 2005, pp. 157–164. Association for Computing Machinery (2005)Google Scholar
  31. 31.
    van der Hoek, W., Wooldridge, M.: Cooperation, Knowledge, and Time: Alternating-Time Temporal Epistemic Logic and its Applications. SL 75(1), 125–157 (2003)zbMATHGoogle Scholar
  32. 32.
    Walther, D., van der Hoek, W., Wooldridge, M.: Alternating-Time Temporal Logic with Explicit Strategies. In: TARK 2007, pp. 269–278 (2007)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Fabio Mogavero
    • 1
  • Aniello Murano
    • 1
  • Luigi Sauro
    • 1
  1. 1.Università degli Studi di Napoli Federico IIItaly

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