Reasoning about Actions in a Probabilistic Setting

In this paper we present a language to reason about actions in a probabilistic setting and compare our work with earlier work by Pearl. The main feature of our language is its use of static and dynamic causal laws, and use of unknown (or background) variables - whose values are determined by factors beyond our model - in incorporating probabilities. We use two kind of unknown variables: inertial and non-inertial. Inertial unknown variables are helpful in assimilating observations and modeling counterfactuals and causality; while non-inertial unknown variables help characterize stochastic behavior, such as the outcome of tossing a coin, that are not impacted by observations. Finally, we give a glimpse of incorporating probabilities into reasoning with narratives.