Abstract
We consider multi-agent systems where agents actions and beliefs are determined aleatorically, or “by the throw of dice”. This system consists of possible worlds that assign distributions to independent random variables, and agents who assign probabilities to these possible worlds. We present a novel syntax and semantics for such system, and show that they generalise Modal Logic. We also give a sound and complete calculus for reasoning in the base semantics, and a sound calculus for the full modal semantics, that we conjecture to be complete. Finally we discuss some application to reasoning about game playing agents.
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Notes
- 1.
We note this function is not deterministic, but this does not impact the final result.
- 2.
https://en.wikipedia.org/wiki/Pig_(dice_game).
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French, T., Gozzard, A., Reynolds, M. (2019). A Modal Aleatoric Calculus for Probabilistic Reasoning. In: Khan, M., Manuel, A. (eds) Logic and Its Applications. ICLA 2019. Lecture Notes in Computer Science(), vol 11600. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-58771-3_6
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