Reasoning about Choice

  • Wiebe van der Hoek
  • Nicolas Troquard
  • Michael Wooldridge
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8068)


We present a logic for reasoning about choice. Choice ctl (c-ctl) extends the well-known branching-time temporal logic ctl with choice modalities, “\(\Diamond\)” and “□”. An example c-ctl formula is \(\Diamond\) AF happy, asserting that there exists a choice that will lead to happiness. c-ctl is related to both stit logics and temporal cooperation logics such as atl, but has a much simpler and (we argue) more intuitive syntax and semantics. After presenting the logic, we investigate the properties of the language. We characterise the complexity of the c-ctl model checking problem, investigate some validities, and propose multi-agent extensions to the logic.


Model Check Modal Logic Transition Relation Choice Modality Deontic Logic 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abdou, J., Keiding, H.: Effectivity Functions in Social Choice Theory. Kluwer Academic Publishers, Dordrecht (1991)CrossRefGoogle Scholar
  2. 2.
    Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. Journal of the ACM 49(5), 672–713 (2002)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Anscombe, G.E.M.: Intention, 2nd edn. Blackwell (1963)Google Scholar
  4. 4.
    Belnap, N., Perloff, M.: Seeing to it that: a canonical form for agentives. Theoria 54, 175–199 (1988)CrossRefGoogle Scholar
  5. 5.
    Belnap, N., Perloff, M., Xu, M.: Facing the future: agents and choices in our indeterminist world, Oxford (2001)Google Scholar
  6. 6.
    Bennett, J.: Events and their names. Hackett Publishing Company, Indianapolis (1988)Google Scholar
  7. 7.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)MATHGoogle Scholar
  8. 8.
    Bratman, M.: Intentions, plans, and practical reason. Harvard University Press, Cambridge (1987)Google Scholar
  9. 9.
    Broersen, J.: CTL.STIT: enhancing ATL to express important multi-agent system verification properties. In: Proceedings of AAMAS 2010 (2010)Google Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    Broersen, J., Herzig, A., Troquard, N.: Embedding Alternating-time Temporal Logic in Strategic STIT Logic of Agency. Journal of Logic and Computation 16(5), 559–578 (2006)MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Broersen, J., Herzig, A., Troquard, N.: Normal coalition logic and its conformant extension. In: Samet, D. (ed.) Proceedings of the Eleventh Conference Theoretical Aspects of Rationality and Knowledge (TARK), pp. 42–51. Presses universitaires de Louvain, Brussels (2007)Google Scholar
  13. 13.
    Chellas, B.: The Logical Form of Imperatives. Perry Lane Press, Stanford (1969)Google Scholar
  14. 14.
    Chellas, B.F.: On bringing it about. Journal of Philosophical Logic 24(6), 563–571 (1995)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. The MIT Press, Cambridge (2000)Google Scholar
  16. 16.
    Davidson, D.: The Logical Form of Action Sentences. In: Rescher, N. (ed.) The Logic of Decision and Action, pp. 81–120. University of Pittsburgh Press (1967)Google Scholar
  17. 17.
    Dennett, D.C.: Intentional systems. Journal of Philosophy, 68(4) (1971)Google Scholar
  18. 18.
    Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science Volume B: Formal Models and Semantics, pp. 996–1072. Elsevier Science Publishers B.V, Amsterdam (1990)Google Scholar
  19. 19.
    Horty, J.: Agency and Deontic Logic. Oxford University Press, Oxford (2001)MATHCrossRefGoogle Scholar
  20. 20.
    Meyer, J.-J.C., Wieringa, R.J. (eds.): Deontic Logic in Computer Science — Normative System Specification. John Wiley & Sons (1993)Google Scholar
  21. 21.
    Müller, T.: On the formal structure of continuous action. In: Schmidt, R., Pratt-Hartmann, I., Reynolds, M. (eds.) AiML-2004: Advances in Modal Logic, pp. 277–286 (2004)Google Scholar
  22. 22.
    Pauly, M.: Logic for Social Software. PhD thesis, University of Amsterdam, ILLC Dissertation Series 2001-10 (2001)Google Scholar
  23. 23.
    Schnoebelen, P.: The complexity of temporal logic model checking. In: Balbiani, P., Suzuki, N.-Y., Wolter, F., Zakharyascev, M. (eds.) Advanced in Modal Logic, vol. 4, pp. 393–436. King’s College Publications, London (2003)Google Scholar
  24. 24.
    Troquard, N.: Independent agents in branching-time. PhD thesis, Univ. of Toulouse & Univ. of Trento (2007)Google Scholar
  25. 25.
    Troquard, N., Trypuz, R., Vieu, L.: Towards an ontology of agency and action: From STIT to OntoSTIT+. In: Bennett, B., Fellbaum, C. (eds.) International Conference on Formal Ontology in Information Systems (FOIS), Baltimore, Maryland, USA. Frontiers in Artificial Intelligence and Applications, vol. 150, pp. 179–190. IOS Press,Google Scholar
  26. 26.
    van der Hoek, W., Roberts, M., Wooldridge, M.: Social laws in alternating time: Effectiveness, feasibility, and synthesis. Synthese 156(1), 1–19 (2007)MathSciNetMATHCrossRefGoogle Scholar
  27. 27.
    van der Hoek, W., Wooldridge, M.: On the logic of cooperation and propositional control. Artificial Intelligence 64, 81–119 (2005)Google Scholar
  28. 28.
    Vendler, Z.: Verbs and times. Philosophical Review 66, 143–160 (1957)CrossRefGoogle Scholar
  29. 29.
    Verkuyl, H.: A Theory of Aspectuality. Cambridge University Press (1993)Google Scholar
  30. 30.
    von Kutschera, F.: Bewirken. Erkenntnis 24(3), 253–281 (1986)CrossRefGoogle Scholar
  31. 31.
    von Wright, G.H.: Norm and Action: A Logical Inquiry. Routledge & Kegan Paul, London (1963)Google Scholar
  32. 32.
    von Wright, G.H.: Deontic logic. Mind 60(237), 1–15 (1951)CrossRefGoogle Scholar
  33. 33.
    Wooldridge, M.: Reasoning about Rational Agents. The MIT Press, Cambridge (2000)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Wiebe van der Hoek
    • 1
  • Nicolas Troquard
    • 2
  • Michael Wooldridge
    • 3
  1. 1.University of LiverpoolUK
  2. 2.Institute of Cognitive Sciences and Technologies (ISTC-CNR)Italy
  3. 3.University of OxfordUK

Personalised recommendations