将因果独立性引入价值理论，建立价值与因果的统一框架。
A Causal Markov Condition for Value
- 提出价值因果马尔可夫条件（v-CMC），连接因果图与效用结构。
- 证明v-CMC局部、全局与分解形式等价，推导出广义贝尔曼递归。
- 支持跨因果场景的效用模块化传递与更新，适合强化学习研究者。
本文提出一种价值领域的因果独立性原则——价值因果马尔可夫条件（v-CMC），并构建了因果与效用关联的理论基础。在动机本地化v-CMC后，引入概率-价值对偶性，将标准因果推断结果映射到价值领域。具体地，提出了v-CMC的局部、全局与分解版本，并证明其等价性。定义了v-分离，并证明其对条件价值独立性具有完全性和可靠性。此外，从v-CMC中推导出贝尔曼型递归，将标准线性链上的贝尔曼方程推广至因果有向无环图（DAG）。最后，展示了v-CMC如何支持效用信息在不同因果情境间的模块化迁移与更新，并开发了因果结构化效用获取及规范影响图构建算法。
原文摘要 · Abstract (English)
This paper proposes a causal independence principle for value -- the value Causal Markov Condition (v-CMC) -- and develops the conceptual and mathematical foundations of a "causal value theory" linking causality and utility. After motivating a local formulation of the v-CMC, we introduce a probability-value duality that translates standard causal-inference results into the value setting. In particular, we formulate local, global, and decomposition versions of the v-CMC and prove their equivalence. We also define v-separation and show that it is sound and complete for conditional value independence. Furthermore, we derive a Bellman-type recursion as a special case of the v-CMC, thereby generalizing standard Bellman recursion from linear chains to causal DAGs. Finally, we show how the v-CMC supports modular transfer and updating of utility information across causal contexts and develop algorithms for causally structured utility elicitation and canonical influence-diagram construction.
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