Epistemic Probability Logic Simplified

We propose a simplified logic for reasoning about (multi-agent) epistemic probability models, and for epistemic probabilistic model checking. Epistemic probability models are multi-agent Kripke models that assign to each agent an equivalence relation on worlds, together with a function from worlds to positive rationals (a lottery). The difference with the usual approach is that probability is linked to knowledge rather than belief, and that knowledge is equated with certainty. A first contribution of the paper is a comparison of a semantics for epistemic probability in terms of models with multiple lotteries and models with a single lottery. We give a proof that multiple lottery models can always be replaced by single lottery models. As multiple lotteries represent multiple subjective probabilities, our result connects subjective and intersubjective probability. Next, we define an appropriate notion of bisimulation, and use it to prove an adaptation of the Hennessy-Milner Theorem and to prove that some finite multiple lottery models only have infinite single lottery counterparts. We then prove completeness, and state results about model checking complexity. In particular, we show the PSPACE-completeness of the model checking in the dynamic version with action models. The logic is designed with model checking for epistemic probability logic in mind; a prototype model checker for it exists. This program can be used to keep track of information flow about aleatory acts among multiple agents.