Formalizing Kantian Ethics: Formula of the Universal Law Logic (FULL)

Moral cognition has traditionally been modeled as adherence to fixed ethical theories--deontology, consequentialism, virtue ethics--implemented as static rules or value functions. We propose Bounded Morality, a formal framework for analyzing the computational demands of moral problems faced by finite agents. Extending Herbert Simon's notion of bounded rationality, we formalize moral situations along two orthogonal dimensions: moral breadth, the scope of entities treated as morally relevant, and moral depth, the inferential integration required to evaluate their interactions. Limited resources impose an unavoidable tradeoff between these dimensions, defining a feasible space of moral computation. Within this space, ethical theories correspond to locally efficient strategies adapted to different demand regimes rather than competing accounts of moral truth. The framework yields a formal notion of moral regret and moral progress under constraint, and implies that moral alignment in artificial systems depends on the scaling and allocation of moral reasoning capacity rather than on direct imitation of human judgments.

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.

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.