超越有向无环图：因果零点与因果微分方程
Beyond Directed Acyclic Graphs: Causal Zeros and Causal Differential Equations
中文总结 AI 辅助
研究珀尔结构因果模型的限制，针对对称物理经济约束及有限传播状态空间系统的问题，通过扩展因果模型和因果微分方程，添加激活算子等方法，给出扩展do-演算等内容，突破现有框架限制。
中文摘要 AI 辅助
珀尔的结构因果模型（SCM）框架基于有向无环图（DAG）和do-演算，是因果推理的主导形式语言。但它有两个结构限制：每个关系必须预先指定为有向因果边，且禁止反馈循环。本文研究了两类对这些限制构成挑战的现象。首先，对称的物理和经济约束，如理想气体定律，没有内在因果方向，方向仅在干预下出现，且求解的变量必须作为干预的一部分指定。我们通过添加激活算子，在扩展因果模型中将此类约束形式化为因果零点，并满足局部可解性和图可容许性条件。其次，对于这里考虑的有限传播状态空间系统，我们将明显的瞬时循环视为抑制时间的产物，并在因果微分方程（CDE）中建立因果零点和反馈的基础。在这些方程中，瞬态状态是时间展开的无环因果过程，因果零点作为吸引平衡流形的定义函数出现；周期和混沌吸引子定义了相同动力学的进一步状态，通过相对于吸引子的干预来处理。我们给出了扩展的do-演算、可识别性条件、反事实语义和开放问题。
英文摘要
Pearl's structural causal model (SCM) framework, built on directed acyclic graphs (DAGs) and the do-calculus, is the dominant formal language for causal reasoning. Yet it carries two structural restrictions: every relationship must be pre-specified as a directed causal edge, and feedback cycles are forbidden. This paper examines two classes of phenomena that strain these restrictions. First, symmetric physical and economic constraints, the ideal gas law being the canonical case, carry no intrinsic causal direction. Direction emerges only under intervention, and which variable is solved for must be specified as part of the intervention. We formalize such constraints as causal zeros within an Extended Causal Model by adding an activation operator, subject to local solvability and graph-admissibility conditions. Second, for the class of finite-propagation state-space systems considered here, we treat apparent instantaneous cycles as artifacts of suppressed time and ground both causal zeros and feedback in Causal Differential Equations (CDEs). In these, the transient regime is a time-unrolled acyclic causal process, and causal zeros arise as the defining functions of attracting equilibrium manifolds; periodic and chaotic attractors define further regimes of the same dynamics, treated through attractor-relative intervention. We give the extended do-calculus, identifiability conditions, counterfactual semantics, and open problems.
