Abstract
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.
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References
Balbiani, P., Herzig, A., Troquard, N.: Alternative axiomatics and complexity of deliberative stit theories. Journal of Philosophical Logic (2007)
Belnap, N., Perloff, M., Xu, M.: Facing the future: agents and choices in our indeterminist world. Oxford (2001)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press, Cambridge (2001)
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)
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)
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)
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)
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 Systems
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)
Pauly, M.: A modal logic for coalitional power in games. Journal of Logic and Computation 12(1), 149–166 (2002)
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Broersen, J.M. (2011). Probabilistic Stit Logic. In: Liu, W. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2011. Lecture Notes in Computer Science(), vol 6717. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22152-1_44
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DOI: https://doi.org/10.1007/978-3-642-22152-1_44
Publisher Name: Springer, Berlin, Heidelberg
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