Pearl's Causal Hierarchy (PCH) is a central framework for reasoning about probabilistic, interventional, and counterfactual statements, yet the satisfiability problem for PCH formulas is computationally intractable in almost all classical settings. We revisit this challenge through the lens of parameterized complexity and identify the first gateways to tractability. Our results include fixed-parameter and XP-algorithms for satisfiability in key probabilistic and counterfactual fragments, using parameters such as primal treewidth and the number of variables, together with matching hardness results that map the limits of tractability. Technically, we depart from the dynamic programming paradigm typically employed for treewidth-based algorithms and instead exploit structural characterizations of well-formed causal models, providing a new algorithmic toolkit for causal reasoning.

翻译：Pearl的因果层次结构（PCH）是推理概率性、干预性和反事实性陈述的核心框架，然而在几乎所有经典设定下，PCH公式的可满足性问题在计算上都是难解的。我们通过参数化复杂度的视角重新审视这一挑战，并首次识别出通向可解性的通路。我们的研究成果包括针对关键概率性和反事实性片段可满足性的固定参数算法与XP算法，这些算法采用原始树宽和变量数量等参数，同时辅以界定可解性边界的匹配硬度结果。在技术层面，我们突破了通常用于基于树宽算法的动态规划范式，转而利用良构因果模型的结构特征，为因果推理提供了全新的算法工具集。