# An Algebraic Exposition of the Theory of Dyadic Morality

arXiv: https://arxiv.org/abs/2605.16153 · HTML: https://mlsanity.com/paper/2605.16153/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 6 of 6)

- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Generative Language Models Exhibit Social Identity Biases](https://mlsanity.com/paper/2310.15819/) (2023)
- [Rethinking Machine Ethics -- Can LLMs Perform Moral Reasoning through the Lens of Moral Theories?](https://mlsanity.com/paper/2308.15399/) (2023)
- [This human study did not involve human subjects: Validating LLM simulations as behavioral evidence](https://mlsanity.com/paper/2602.15785/) (2026)
- [Deep Binding of Language Model Virtual Personas: a Study on Approximating Political Partisan Misperceptions](https://mlsanity.com/paper/2504.11673/) (2025)
- [When Trust is Zero Sum: Automation Threat to Epistemic Agency](https://mlsanity.com/paper/2408.08846/) (2024)

## Abstract (arXiv)

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.