We define an extension of stit logic that encompasses subjective probabilities representing beliefs about simultaneous choice exertion of other agents. This semantics enables us to express that an agent sees to it that a condition obtains under a minimal chance of success. We first define the fragment of XSTIT where choice exertion is not collective. Then we add effect probability lower bounds to the stit syntax, and define the semantics in terms of subjective probabilities concerning choice exertion of other agents. We show how the resulting probabilistic stit logic faithfully generalizes the non-probabilistic XSTIT fragment.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Balbiani, P., Herzig, A., Troquard, N.: Alternative axiomatics and complexity of deliberative stit theories. Journal of Philosophical Logic (2007)Google Scholar
  2. 2.
    Belnap, N., Perloff, M., Xu, M.: Facing the future: agents and choices in our indeterminist world. Oxford (2001)Google Scholar
  3. 3.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press, Cambridge (2001)CrossRefMATHGoogle Scholar
  4. 4.
    Broersen, J.M., 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)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Broersen, J.M., Herzig, A., Troquard, N.: A normal simulation of coalition logic and an epistemic extension. In: Samet, D. (ed.) Proceedings Theoretical Aspects Rationality and Knowledge (TARK XI), Brussels, pp. 92–101. ACM Digital Library (2007)Google Scholar
  6. 6.
    Conradie, W., Goranko, V., Vakarelov, D.: Algorithmic correspondence and completeness in modal logic I: The core algorithm SQEMA. Logical Methods in Computer Science 2(1), 1–26 (2006)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science. Formal Models and Semantics, vol. B, ch. 14, pp. 996–1072. Elsevier Science, Amsterdam (1990)Google Scholar
  8. 8.
    Jamroga, W.: A temporal logic for markov chains. In: AAMAS 2008: Proceedings of the 7th International Joint Conference on Autonomous Agents and Multiagent Systems, Richland, SC, pp. 697–704 (2008); International Foundation for Autonomous Agents and Multiagent SystemsGoogle Scholar
  9. 9.
    Kooi, B.P., Tamminga, A.M.: Conflicting obligations in multi-agent deontic logic. In: Goble, L., Meyer, J.-J.C. (eds.) DEON 2006. LNCS (LNAI), vol. 4048, pp. 175–186. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Pauly, M.: A modal logic for coalitional power in games. Journal of Logic and Computation 12(1), 149–166 (2002)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jan M. Broersen
    • 1
  1. 1.Department of Information and Computing SciencesUtrecht UniversityThe Netherlands

Personalised recommendations