We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of expressing quantitative probabilistic reasoning -- including conditional independence and Bayesian inference -- the second encoding do-calculus reasoning for causal effects, and the third capturing a fully expressive do-calculus for arbitrary counterfactual queries. We give a corresponding series of finitary axiomatizations complete over both structural causal models and probabilistic programs, and show that satisfiability and validity for each language are decidable in polynomial space.

翻译：我们提议将关联、干预和反事实的三级因果等级正规化为一系列概率逻辑语言。 我们的语言具有严格的直率性,能够表达量化概率推理(包括有条件的独立和巴伊西亚推理)的第一种能力是量化概率推理(包括有条件的独立和巴伊西亚推理 ), 第二种因果计算推理,第三种为任意反事实质询捕捉了完全清晰的量度计算。 我们对结构性因果模型和概率方案都给出了相应的一系列有鳍分解分解法,并表明每种语言的可裁判性和有效性在多元空间中是可以裁断的。