Logics for Reasoning About Strategic Abilities in Multi-player Games

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8972)


We introduce and discuss basic concepts, ideas, and logical formalisms used for reasoning about strategic abilities in multi-player games. In particular, we present concurrent game models and the alternating time temporal logic \(\mathsf {ATL}^{*}\) and its fragment \(\mathsf {ATL}\). We discuss variations of the language and semantics of \(\mathsf {ATL}^{*}\) that take into account the limitations and complications arising from incomplete information, perfect or imperfect memory of players, reasoning within dynamically changing strategy contexts, or using stronger, constructive concepts of strategy. Finally, we briefly summarize some technical results regarding decision problems for some variants of \(\mathsf {ATL}\).


Logics Game theory Strategic reasoning Strategic logic Multi-agent systems Automated reasoning 



We are grateful to the participants in the Workshop on Modelling Strategic Reasoning held in February 2012 in the Lorentz Center, Leiden, and particularly to Nicolas Troquard and Dirk Walther, as well as to the anonymous reviewers, for their valuable comments and suggestions. Wojciech Jamroga acknowledges the support of the National Research Fund (FNR) Luxembourg under the project GALOT (INTER/DFG/12/06), as well as the support of the 7th Framework Programme of the European Union under the Marie Curie IEF project ReVINK (PIEF-GA-2012-626398). The final work of Valentin Goranko on this chapter was done while he was an invited visiting professor at the Centre International de Mathématiques et Informatique de Toulouse.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Nils Bulling
    • 1
  • Valentin Goranko
    • 2
    • 3
  • Wojciech Jamroga
    • 4
    • 5
  1. 1.Department of Intelligent SystemsTU DelftDelftThe Netherlands
  2. 2.Department of PhilosophyStockholm UniversityStockholmSweden
  3. 3.Department of MathematicsUniversity of JohannesburgJohannesburgSouth Africa
  4. 4.Institute of Computer Science, Polish Academy of SciencesWarszawaPoland
  5. 5.Computer Science and Communication Research Unit and Interdisc. Centre on Security, Reliability and TrustUniversity of LuxembourgLuxembourg CityLuxembourg

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