We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose instance formulas allow expressing many tasks in probabilistic and causal inference. The main contribution of this work is establishing the exact computational complexity of these satisfiability problems. We introduce a new natural complexity class, named succ$\exists$R, which can be viewed as a succinct variant of the well-studied class $\exists$R, and show that the problems we consider are complete for succ$\exists$R. Our results imply even stronger algorithmic limitations than were proven by Fagin, Halpern, and Megiddo (1990) and Moss\'{e}, Ibeling, and Icard (2022) for some variants of the standard languages used commonly in probabilistic and causal inference.

研究员从计算复杂性的角度出发，研究了能够完全表达数量化概率推理和因果效应的形式语言。研究集中于可表达许多概率和因果推断任务的可满足性问题，并建立了这些可满足性问题的确切计算复杂性。研究结果表明，一些在概率和因果推断中常用的标准语言的变体的算法限制更强。

关于概率和因果推理的困难程度