Abstract
We draw parallels between several closely related logics that combine — in different proportions — elements of game theory, computation tree logics, and epistemic logics to reason about agents and their abilities. These are: the coalition game logics CL and ECL introduced by Pauly in 2000, the alternating-time temporal logic ATL developed by Alur, Henzinger and Kupferman between 1997 and 2002, and the alternating-time temporal epistemic logic ATEL by van der Hoek and Wooldridge (2002). In particular, we establish some subsumption and equivalence results for their semantics, as well as interpretation of the alternating-time temporal epistemic logic into ATL.
The focus in this paper is on models: alternating transition systems, multi-player game models (alias concurrent game structures) and coalition effectivity models turn out to be intimately related, while alternating epistemic transition systems share much of their philosophical and formal apparatus. Our approach is constructive: we present ways to transform between different types of models and languages.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abdou, J.: 1998, ‘Rectangularity and Tightness: A Normal Form Characterization of Perfect Information Extensive Game Forms’, Mathematics and Operations Research 23(3).
Alur, R., T. A. Henzinger, and O. Kupferman: 1997, ‘Alternating-Time Temporal Logic’, in Proceedings of the 38th Annual Symposium on Foundations of Computer Science (FOCS), IEEE Computer Society Press, pp. 100–109. Available at http://www.citeseer.nj.nec.com/170985.html.
Alur, R., T. A. Henzinger, and O. Kupferman: 1998a, ‘Alternating-Time Temporal Logic’, Lecture Notes in Computer Science 1536, 23–60. Available at http://wwwciteseer.nj.nec.com/174802.html.
Alur, R., T. A. Henzinger, and O. Kupferman: 2002, ‘Alternating-Time Temporal Logic’, Journal of the ACM 49, 672–713. Updated, improved, and extended text. Available at http://wwwwww.cis.upenn.edu/alur/Jacm02.pdf.
Alur, R., T. A. Henzinger, O. Kupferman, and M. Vardi: 1998b, ‘Alternating Refinement Relations’, in CONCUR’98.
Aumann, R. and S. Hart (eds.): 1992, Handbook of Game Theory with Economic Applications, Vol. 1, Elsevier/North-Holland.
Chandra, A., D. Kozen, and L. Stockmeyer: 1981, ‘Alternation’, Journal of the ACM 28(1), 114–133.
Emerson, E. A.: 1990, ‘Temporal and Modal Logic’, in J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, Vol. B, Elsevier, pp. 995–1072.
Fagin, R., J. Y. Halpern, Y. Moses, and M. Y. Vardi: 1995, Reasoning about Knowledge, MIT Press, Cambridge, MA.
Gerbrandy, J.: 1999, ‘Bisimulations on Planet Kripke’, Ph.D. thesis, University of Amsterdam.
Goranko, V.: 2001, ‘Coalition Games and Alternating Temporal Logics’, in J. van Benthem (ed.), Proceedings of the 8th Conference on Theoretical Aspects of Rationality and Knowledge (TARK VIII), Morgan Kaufmann, pp. 259–272, Corrected version. Available at http://wwwhttp://general.rau.ac.za/maths/goranko/papers/gltl31.pdf.
Goranko, V. and G. van Drimmelen: 2003, ‘Complete Axiomatization and Decidability Submitted of the Alternating-Time Temporal Logic’.
Hart, S.: 1992, ‘Games in Extensive and Strategic Forms’, in R. Aumann and S. Hart (eds.), Handbook of Game Theory with Economic Applications, Vol. 1, Elsevier/North-Holland, pp. 19–40.
Huth, M. and M. Ryan: 2000, Logic in Computer Science: Modelling and Reasoning about Systems, Cambridge University Press.
Jamroga, W.: 2003, ‘Some Remarks on Alternating Temporal Epistemic Logic’, in B. Dunin-Keplicz and R. Verbrugge (eds.), Proceedings of Formal Approaches to Multi-Agent Systems (FAMAS 2003), pp. 133–140.
Jamroga, W. and W. van der Hoek: 2003, ‘Agents that Know how to Play’, submitted.
Lomuscio, A.: 1999, ‘Information Sharing among Ideal Agents’, Ph.D. thesis, University of Birmingham.
Moore, R.: 1985, ‘A Formal Theory of Knowledge and Action’, in J. Hobbs and R. Moore (eds.), Formal Theories of the Commonsense World, Ablex Publishing Corporation.
Morgenstern, L.: 1991, ‘Knowledge and the Frame Problem’, International Journal of Expert Systems 3(4).
Osborne, M. and A. Rubinstein: 1994, A Course in Game Theory, MIT Press, Cambridge, MA.
Parikh, R.: 1985, ‘The Logic of Games and its Applications’, Ann. of DiscreteMathematics 24, 111–140.
Pauly, M.: 2000a, ‘Game Logic for Game Theorists’, Technical Report INS-R0017, CWI.
Pauly, M.: 2000b, ‘A Logical Framework for Coalitional Effectivity in Dynamic Procedures’, in Proceedings of the Conference on Logic and the Foundations of Game and Decision Theory (LOFT4), To appear in Bulletin of Economics Research.
Pauly, M.: 2001, ‘Logic for Social Software’, Ph.D. thesis, University of Amsterdam.
Pauly, M.: 2002, ‘A Modal Logic for Coalitional Power in Games’, Journal of Logic and Computation 12(1), 149–166.
Quine, W.: 1956, ‘Quantifiers and Propositional Attitudes’, Journal of Philosophy 53, 177–187.
Rao, A. and M. Georgeff: 1991, ‘Modeling Rational Agents within a BDI-Architecture’, Proceedings of the 2nd International Conference on Principles of Knowledge Representation and Reasoning, pp. 473–484.
Schild, K.: 2000, ‘On the Relationship between BDI Logics and Standard Logics of Concurrency’, Autonomous Agents and Multi Agent Systems pp. 259–283.
Schnoebelen, P.: 2003, ‘The Complexity of Temporal Model Checking’, Advances in Modal Logics, Proceedings of AiML 2002, World Scientific.
van Benthem, J.: 2000, ‘Logic and Games’, Technical Report X-2000-03, ILLC.
van der Hoek, W. and R. Verbrugge: 2002, ‘Epistemic Logic: A Survey’, Game Theory and Applications 8, 53–94.
van der Hoek, W. and M. Wooldridge: 2002, ‘Tractable Multiagent Planning for Epistemic Goals’, in C. Castelfranchi and W. Johnson (eds.): Proceedings of the First International Joint Conference on Autonomous Agents and Multi-Agent Systems (AAMAS-02), ACM Press, New York, pp. 1167–1174.
van der Hoek, W. and M. Wooldridge: 2003a, ‘Cooperation, Knowledge and Time — Alternating-time Temporal Epistemic Logic and its Applications’, Studia Logica 75(1), 125–157.
van der Hoek, W. and M. Wooldridge: 2003b, ‘Towards a Logic of Rational Agency’, Logic Journal of the IGPL 11(2), 135–160.
van Drimmelen, G.: 2003, ‘Satisfiability in Alternating-Time Temporal Logic’, in Proceedings of LICS’2003 IEEE Computer Society Press, pp. 208–217.
van Otterloo, S., W. van der Hoek, and M. Wooldridge: 2003, ‘Knowledge as Strategic Ability’, Electronic Lecture Notes in Theoretical Computer Science 85(2).
von Neumann, J. and O. Morgenstern: 1944, Theory of Games and Economic Behaviour, Princeton University Press, Princeton, NJ.
Wooldridge, M.: 2000, Reasoning about Rational Agents, MIT Press, Cambridge, MA.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Kluwer Academic Publishers
About this chapter
Cite this chapter
Goranko, V., Jamroga, W. (2004). Comparing Semantics of Logics for Multi-Agent Systems. In: Information, Interaction and Agency. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4094-6_3
Download citation
DOI: https://doi.org/10.1007/1-4020-4094-6_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3600-2
Online ISBN: 978-1-4020-4094-8
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)