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：我们提出了一种形式化语言，用于描述和解释统计因果性。具体而言，我们定义了统计因果语言（StaCL），以表达因果效应并指定因果推断所需的条件。StaCL通过模态算子引入干预操作，在克里普克模型的不同可能世界中表达概率分布之间的因果性质。我们使用StaCL公式形式化了概率分布、干预操作和因果谓词的公理。这些公理具有足够的表达能力，可以推导出珀尔do-演算的规则。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。