Many tasks in statistical and causal inference can be construed as problems of \emph{entailment} in a suitable formal language. We ask whether those problems are more difficult, from a computational perspective, for \emph{causal} probabilistic languages than for pure probabilistic (or "associational") languages. Despite several senses in which causal reasoning is indeed more complex -- both expressively and inferentially -- we show that causal entailment (or satisfiability) problems can be systematically and robustly reduced to purely probabilistic problems. Thus there is no jump in computational complexity. Along the way we answer several open problems concerning the complexity of well known probability logics, in particular demonstrating the $\exists\mathbb{R}$-completeness of a polynomial probability calculus, as well as a seemingly much simpler system, the logic of comparative conditional probability.

翻译：在统计和因果推断中，许多任务可以被理解为在适当的逻辑语言框架下的\emph{蕴涵}问题。我们探讨：从计算角度来看，这些问题对于\emph{因果}概率语言是否比纯概率（或“关联性”）语言更具难度。尽管因果推理在表达能力和推理机制上确实更为复杂，但我们证明，因果蕴涵（或可满足性）问题可以系统且鲁棒地归约为纯概率问题，因此计算复杂度并未出现跳跃。在此过程中，我们解答了若干关于经典概率逻辑复杂性的开放问题，特别是证明了多项式概率演算系统以及一个看似更简化的系统——比较条件概率逻辑——均属于$\exists\mathbb{R}$-完全问题。