用代数方法形式化二人道德判断模型，让AI更懂人类道德推理。
An Algebraic Exposition of the Theory of Dyadic Morality
- 基于因果建模构建三人心理运算符，模拟人类道德判断机制。
- 揭示多节点情境下通过节点压缩与顺序处理实现道德认知扩展。
- 适用于AI政策设计、故障沟通等场景，支持可解释的道德计算。
本文提供了一种关于二元道德理论（TDM）的代数表述，该理论以一个意图主体对脆弱患者造成伤害的两节点模板为基础。通过结构因果建模（SCM）符号，我们形式化了三种心理算子：类型化算子、补全算子和依赖效价的推断机制，将标准SCM扩展以捕捉人们在约束条件下进行道德判断的方式。针对TDM二元局限带来的可扩展性挑战，我们展示了道德认知如何通过节点坍缩和顺序处理压缩多节点情景。基于此代数框架，我们演示了其在人工智能政策设计中的具体应用：检测冲突义务、设计保持用户自主性的助人策略，以及将失败后沟通作为因果干预。最后，建议采用范围限定、情境敏感的心智感知测量，而非普遍平均，来实证操作该理论。这一代数形式化使神经符号系统能够以数学严谨且符合人类道德认知的方式计算道德判断。
原文摘要 · Abstract (English)
This paper provides an algebraic exposition of the theory of dyadic morality (TDM), a psychological model of moral judgment grounded in a simple two-node template: an intentional agent causing harm to a vulnerable patient. We formalize TDM using structural causal modeling (SCM) notation and identify three psychological operators (typecasting operator, completion operator, and valence-dependent inference mechanism) that extend standard SCM to capture how people compute moral judgments under constraints. We address scalability challenges arising from TDM's dyadic limitation, showing how moral cognition compresses multi-node scenarios through node collapse and sequential processing. Drawing on this algebraic framework, we demonstrate concrete applications to AI policy design: detecting conflicting obligations, structuring helpfulness policies to preserve user agency, and designing post-failure communication as causal interventions. Finally, we recommend scoped, contextual measurement of mind perception over universal averaging to operationalize the theory empirically. This algebraic formalization enables neurosymbolic AI systems to compute morality in a way that is both mathematically rigorous and faithful to human moral cognition.
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