An Algebraic Exposition of the Theory of Dyadic Morality

TL;DR

This paper formalizes the theory of dyadic morality using algebraic and causal modeling, enabling AI systems to better understand and compute human-like moral judgments.

Contribution

It introduces an algebraic framework with psychological operators to model moral cognition and demonstrates applications in AI policy design and measurement.

Findings

Formalized TDM using structural causal models

Identified three psychological operators extending SCM

Applied framework to AI policy and measurement

Abstract

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.