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.

翻译：我们提出了一种用于描述和解释统计因果的形式化语言。具体而言，我们定义了统计因果语言（StaCL），用于表达因果效应并指定因果推断的要求。StaCL引入了干预的模态算子，以在Kripke模型的不同可能世界中表达概率分布之间的因果属性。我们利用StaCL公式形式化了关于概率分布、干预和因果谓词的公理。这些公理具有足够的表达能力，可以推导出Pearl的do-演算规则。最后，我们通过实例证明，StaCL可用于指定和解释统计因果推断的正确性。