  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.
