An Algebraic Exposition of the Theory of Dyadic Morality

Abstract

to be pro-social (Abdulhai et al. 2024). These different ap- arXiv:2605.16153v1 [cs.AI] 15 May 2026 proaches can be operationalized in guiding the behaviors of This paper provides an algebraic exposition of the theory AI agents with varying ease due to their inherent underly- of dyadic morality (TDM), a psychological model of moral ing structure. However, none of them are straightforwardly judgment grounded in a simple two-node template: an inten- mechanistic, symbolic, and algebraic in a way that allows tional agent causing harm to a vulnerable patient. We formal- ize TDM using structural causal modeling (SCM) notation for moral reasoning by AI agents in novel situations or with and identify three psychological operators (typecasting oper- parameterizations to permit moral judgments mediated by a ator, completion operator, and valence-dependent inference particular public’s perspectives. mechanism) that extend standard SCM to capture how peo- In contrast, the theory of dyadic morality (TDM) presents ple compute moral judgments under constraints. We address an approach to moral judgment that is readily computable by scalability challenges arising from TDM’s dyadic limitation, neurosymbolic AI systems (Gray, Gray, and Wegner 2007; showing how moral cognition compresses multi-node scenar- Gray and Wegner 2009; Gray, Young, and Waytz 2012; ios through node collapse and sequential processing. Draw- Gray, Waytz, and Young 2012; Wegner and Gray 2017; ing on this algebraic framework, we demonstrate concrete applications to AI policy design: detecting conflicting obliga- Schein and Gray 2018; Gray 2025). Originated and empiri- tions, structuring helpfulness policies to preserve user agency, cally validated by social psychologist Kurt Gray and collab- and designing post-failure communication as causal interven- orators, the basic idea is that all moral reasoning boils down tions. Finally, we recommend scoped, contextual measure- to a simple dyadic (two-n