  We propose a formal language for describing and explaining statistical
causality. Concretely, we define Statistical Causality Language (StaCL) for
expressing causal effects and specifying the requirements for causal inference.
StaCL incorporates modal operators for interventions to express causal
properties between probability distributions in different possible worlds in a
Kripke model. We formalize axioms for probability distributions, interventions,
and causal predicates using StaCL formulas. These axioms are expressive enough
to derive the rules of Pearl's do-calculus. Finally, we demonstrate by examples
that StaCL can be used to specify and explain the correctness of statistical
causal inference.
