Advertisement

Frontiers of Computer Science

, Volume 9, Issue 1, pp 75–86 | Cite as

A complete coalition logic of temporal knowledge for multi-agent systems

  • Qingliang Chen
  • Kaile Su
  • Yong Hu
  • Guiwu Hu
Research Article

Abstract

Coalition logic (CL) is one of the most influential logical formalisms for strategic abilities of multi-agent systems. CL can specify what a group of agents can achieve through choices of their actions, denoted by [C]ϕ to state that a group of agents C can have a strategy to bring about ϕ by collective actions, no matter what the other agents do. However, CL lacks the temporal dimension and thus can not capture the dynamic aspects of a system. Therefore, CL can not formalize the evolvement of rational mental attitudes of the agents such as knowledge, which has been shown to be very useful in specifications and verifications of distributed systems, and has received substantial amount of studies. In this paper, we introduce coalition logic of temporal knowledge (CLTK), by incorporating a temporal logic of knowledge (Halpern and Vardi’s logic of CKL n ) into CL to equip CL with the power to formalize how agents’ knowledge (individual or group knowledge) evolves over the time by coalitional forces and the temporal properties of strategic abilities as well. Furthermore, we provide an axiomatic system for CLTK and prove that it is sound and complete, along with the complexity of the satisfiability problem which is shown to be EXPTIME-complete.

Keywords

coalition logic temporal logic of knowledge complete axiomatization multi-agent systems 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Hoek van der W, Wooldridge M. Multi-agent systems. Handbook of Knowledge Representation. Elsevier Press, 2008, 887–928CrossRefGoogle Scholar
  2. 2.
    Shoham Y, Leyton-Brown K. Multi-agent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, 2008CrossRefGoogle Scholar
  3. 3.
    Wooldridge M. An Introduction to Multiagent Systems. 2nd ed. John Wiley & Sons Press, 2009Google Scholar
  4. 4.
    Wooldridge M. Reasoning about Rational Agents. MIT Press, 2000zbMATHGoogle Scholar
  5. 5.
    Hoek van der W, Wooldridge M. Logics for multi-agent systems. In: Weiss G, ed. Multi-Agent Systems 2nd ed. MIT Press, 2013, 671–810Google Scholar
  6. 6.
    Halpern J Y, Fagin R, Moses Y, Vardi M Y. Reasoning About Knowledge. MIT Press, 1995zbMATHGoogle Scholar
  7. 7.
    Meyer J J C, Hoek van der W. Epistemic Logic for AI and Computer Science (Cambridge Tracts in Theoretical Computer Science). Cambridge University Press, 2004Google Scholar
  8. 8.
    Osborne MJ, Rubinstein A. A Course in Game Theory. The MIT Press, 1994zbMATHGoogle Scholar
  9. 9.
    Pauly M. A modal logic for coalitional power in games. Journal of Logic and Computation, 2002, 12(1): 149–166CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Alur R, Henzinger T A, Kupferman O. Alternating-time temporal logic. Journal of the ACM, 2002, 49(5): 672–713CrossRefMathSciNetGoogle Scholar
  11. 11.
    Broersen J. A complete STIT logic for knowledge and action, and some of its applications. Lecture Notes in Computer Science, 2009, 5397: 47–59CrossRefGoogle Scholar
  12. 12.
    Hoek van der W, Wooldridge M. Cooperation, knowledge, and time: alternating-time temporal epistemic logic and its applications. Studia Logica, 2003, 75(1): 125–157CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Ågotnes T, Alechina N. Epistemic coalition logic: completeness and complexity. In: Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems. 2012, 1099–1106Google Scholar
  14. 14.
    Ågotnes T, Hoek van der W, Wooldridge M. Quantified coalition logic. Synthese, 2008, 165(2): 269–294CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Boella G, Gabbay D M, Genovese V, Torre van der L. Higher-order coalition logic. In: Proceedings of the 19th European Conference on Artificial Intelligence. 2010, 555–560Google Scholar
  16. 16.
    Ågotnes T, Hoek van der W, Wooldridge M. Reasoning about coalitional games. Artificial Intelligence, 2009, 173(1): 45–79CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Troquard N, Walther D. Alternating-time dynamic logic. In: Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems. 2010, 473–480Google Scholar
  18. 18.
    Walther D, Hoek van der W, Wooldridge M. Alternating-time temporal logic with explicit strategies. In: Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge. 2007, 269–278CrossRefGoogle Scholar
  19. 19.
    Seylan I, Jamroga W. Description logic for coalitions. In: Proceedings of the 8th International Joint Conference on Autonomous Agents and Multiagent Systems. 2009, 425–432Google Scholar
  20. 20.
    Bulling N, Dix J, Chesñevar C I. Modelling coalitions: ATL + argumentation. In: Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems. 2008, 681–688Google Scholar
  21. 21.
    Halpern J Y, Vardi M Y. The complexity of reasoning about knowledge and time: extended abstract. In: Proceedings of the 18th Annual ACM Symposium on Theory of Computing. 1986, 304–315Google Scholar
  22. 22.
    Goranko V, Drimmelen van G. Complete axiomatization and decidability of alternating-time temporal logic. Theoretical Computer Science, 2006, 353(1–3): 93–117CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Broersen J, Herzig A, Troquard N. A normal simulation of coalition logic and an epistemic extension. In: Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge. 2007, 92–101CrossRefGoogle Scholar
  24. 24.
    Broersen J, Herzig A, Troquard N. What groups do, can do, and know they can do: an analysis in normal modal logics. Journal of Applied Non-Classical Logics, 2009, 19(3): 261–290CrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    Rapoport A, Chammah A M. Prisoner’s Dilemma. University of Michigan Press, 1965Google Scholar
  26. 26.
    Goranko V, Jamroga W, Turrini P. Strategic games and truly playable effectivity functions. Autonomous Agents and Multi-Agent Systems, 2013, 26(2): 288–314CrossRefGoogle Scholar
  27. 27.
    Pauly M. Logic for Social Software. Dissertation for the Doctoral Degree. University of Amsterdam, 2001Google Scholar
  28. 28.
    Marker D. Model Theory: An Introduction (Graduate Texts in Mathematics, Vol. 217). Springer Press, 2002Google Scholar
  29. 29.
    Ditmarsch van H, Hoek van der W, Kooi B. Dynamic Epistemic Logic. Springer Press, 2007CrossRefGoogle Scholar
  30. 30.
    Vardi M Y. Branching vs. linear time: Final showdown. In: Proceedings of the 7th International Conference on Tools and Algorithms for the Construction and Analysis of Systems. 2001, 1–22CrossRefGoogle Scholar
  31. 31.
    Emerson E A. Temporal and modal logic. Handbook of Theoretical Computer Science (Volume B): Formal Models and Semantics. North-Holland Pub. Co./MIT Press, 1990Google Scholar
  32. 32.
    Ågotnes T, Hoek van der W, Rodríguez-Aguilar J A, Sierra C, Wooldridge M. Multi-modal CTL: completeness, complexity, and an application. Studia Logica, 2009, 92(1): 1–26CrossRefzbMATHMathSciNetGoogle Scholar
  33. 33.
    Belardinelli F, Lomuscio A. First-order linear-time epistemic logic with group knowledge: an axiomatisation of the monodic fragment. Fundamenta Informaticae, 2011, 106(2–4): 175–190zbMATHMathSciNetGoogle Scholar
  34. 34.
    Belardinelli F, Lomuscio A. Interactions between knowledge and time in a first-order logic for multi-agent systems: completeness results. Journal of Artificial Intelligence Research, 2012, 45: 1–45zbMATHMathSciNetGoogle Scholar
  35. 35.
    Lorini E, Schwarzentruber F. A logic for reasoning about counterfactual emotions. Artificial Intelligence, 2011, 175(3–4): 814–847CrossRefzbMATHMathSciNetGoogle Scholar
  36. 36.
    Su K, Sattar A, Governatori G, Chen Q. A computationally grounded logic of knowledge, belief and certainty. In: Proceedings of the 4th International Joint Conference on Autonomous Agents and Multiagent Systems. 2005, 149–156CrossRefGoogle Scholar
  37. 37.
    Wu L, Su K, Sattar A, Chen Q, Su J, Wu W. A complete first-order temporal BDI logic for forest multi-agent systems. Knowledge-Based System, 2012, 27: 343–351CrossRefzbMATHGoogle Scholar
  38. 38.
    Ågotnes T, Hoek van der W, Tennenholtz M, Wooldridge M. Power in normative systems. In: Proceedings of the 8th International Joint Conference on Autonomous Agents and Multiagent Systems. 2009, 145–152Google Scholar
  39. 39.
    Jamroga W, Ågotnes T. Constructive knowledge: what agents can achieve under imperfect information. Journal of Applied Non-Classical Logics, 2007, 17(4): 423–475CrossRefzbMATHMathSciNetGoogle Scholar
  40. 40.
    Bulling N, Jamroga W. Comparing variants of strategic ability: how uncertainty and memory influence general properties of games. Autonomous Agents and Multi-Agent Systems, 2014, 28(3): 474–518CrossRefGoogle Scholar
  41. 41.
    Grädel E. Model-checking games for logics of imperfect information. Theoretical Computer Science, 2013, 493: 2–14CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceJinan UniversityGuangzhouChina
  2. 2.Institute for Integrated and Intelligent SystemsGriffith UniversityBrisbaneAustralia
  3. 3.Institute of Business Intelligence and Knowledge DiscoveryGuangdong University of Foreign StudiesGuangzhouChina
  4. 4.School of Mathematics and StatisticsGuangdong University of Finance and EconomicsGuangzhouChina

Personalised recommendations