We propose a formal language for describing and explaining statistical causality. Concretely, we define Statistical Causality Language (StaCL) for specifying causal effects on random variables. 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 prove and explain the correctness of statistical causal inference.

翻译：我们建议一种正式的语言来描述和解释统计因果关系。具体地说,我们定义统计因果关系语言(StaCL),以具体说明对随机变量的因果关系。StaCL包含干预模式,以表达Kripke模型中不同可能世界的概率分布之间的因果关系。我们正式确定了使用StaCL公式的概率分布、干预和因果前提的轴。这些轴心足够表达出珍珠的“做算法”规则。最后,我们通过实例证明,StaCL可以用来证明和解释统计因果关系推断的正确性。