可满足性在佩尔的因果层级中的可处理性之门
Gateways to Tractability for Satisfiability in Pearl's Causal Hierarchy
AI总结：
本文通过参数化复杂性方法，为佩尔因果层级中的可满足性问题提供了首个可处理性之门，结合固定参数和XP算法，探索了概率性和反事实片段的计算复杂性边界。
摘要：
佩尔的因果层级（PCH）是一个用于推理概率性、干预性和反事实陈述的核心框架，然而在几乎所有经典设置中，PCH公式可满足性问题在计算上都是不可处理的。我们通过参数化复杂性视角重新审视这一挑战，并识别出首个可处理性之门。我们的结果包括针对关键概率性和反事实片段的固定参数和XP算法，使用如原始树宽和变量数量等参数，同时提供了匹配的难度结果，映射出可处理性的极限。技术上，我们脱离通常用于树宽算法的动态规划范式，转而利用良好形成因果模型的结构特征，提供了一种新的因果推理算法工具包。
英文摘要：
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.
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