An Algebraic Exposition of the Theory of Dyadic Morality

Theory of mind (ToM), the capacity to ascribe mental states to others and use those ascriptions for prediction and inference, is widely assumed to be essential for effective human-machine integration. Existing AI-ToM models address \emph{how} to mentalize, but leave the question of when largely unaddressed. The central question is: under what situational and agent-level conditions is ToM engagement causally warranted in conflict? This paper presents a structural causal model formalized as a directed acyclic graph (DAG), treating ToM as a mechanism activated by situational and agent-level conditions rather than as an always-on capacity. The model specifies four exogenous variables capturing situational and agent-level conditions, five endogenous mediators, and a mechanistic ToM node producing engagement states through three distinct causal pathways: a tractability pathway, a reasoning-depth pathway, and an enabling-cause pathway. The primary outcome is epistemic accuracy, which decouples social reasoning from behavioral policy and generalizes across social phenomena beyond conflict. The framework gives AI systems a principled, resource-rational decision procedure for mentalizing, with implications for efficiency, trust, and the development of robust artificial social intelligence. Simulation validation, empirical human-machine teaming studies, and ethical considerations arising from conflict-optimized mentalizing are discussed.

Existing LLM moral benchmarks usually ask which isolated moral act, value, or foundation a model prefers. This is useful but incomplete. Realistic judgments often require a model to combine several moral signals within the same option. We introduce Moral Trolley Arena, a two-stage blind ELO benchmark for measuring how LLMs compose moral evidence. The single-scene arena first calibrates individual moral acts from a 229-scenario corpus across five Moral Foundations Theory foundations; the composite arena then combines calibrated acts into two-act moral items over a controlled intensity grid and measures the resulting composite preferences. Across ten frontier models, composite judgments are largely predicted by component act strength, but the relation is consistently compressed rather than simply additive. Models also show non-additive intensity anchoring, bounded foundation-specific residuals after component control, and highly convergent composite preference surfaces across providers. These results suggest that moral audits should measure composition rules for moral evidence, not only rankings over isolated acts.

Autonomous agents operating in shared environments must make decisions that affect multiple individuals with potentially conflicting interests. We propose a formal framework for moral decision-making grounded in Scanlon's contractualism, an ethical theory that evaluates the permissibility of actions in terms of principles that no one could reasonably reject. To operationalise contractualist reasoning, we use ASPIC+, a structured argumentation framework, extended with value-based filtering to model how each agent's values determine which reasons are morally relevant in the first place. The result is a Contractualist Argumentation Framework in which agents' reasons are formally represented, compared, and evaluated through argumentation semantics. We illustrate the approach through a worked example in a domestic setting and discuss its relation to existing value-based argumentation approaches.