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

arXiv cs.AI / 4/17/2026

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Key Points

The paper proposes a formal logic framework for machine ethics aimed at building Artificial Moral Agents (AMAs) that can evaluate actions more safely.
It argues that prior approaches that hard-code moral axioms (like “do not harm”) miss two key aspects: the agent’s underlying purposes and the assumption that human moral intuition can be fully enumerated.
Focusing on Kantian ethics, the authors introduce the Formula of the Universal Law Logic (FULL), a multi-sorted quantified modal logic that formalizes Kant’s categorical imperative (FUL) along with related notions such as causality and agency.
The authors show, using three Kantian examples, that FULL can reason about whether an agent’s actions are permissible for specific purposes without requiring built-in moral intuition, assuming the system has sufficient non-normative background knowledge.
The work is presented as a step toward more robust, autonomous AMAs and a more rigorous formal understanding of Kantian moral reasoning.

Abstract

The field of machine ethics aims to build Artificial Moral Agents (AMAs) to better understand morality and make AI agents safer. To do so, many approaches encode human moral intuition as a set of axioms on actions e.g., do not harm, you must help others. However, this introduces (at least) two limitations for future AMAs. First, it does not consider the agent's purposes in performing the action. Second, it assumes that we humans can enumerate our moral intuition. This paper explores formalizing a moral procedure that alleviates these two limitations. We specifically consider Kantian ethics and present a multi-sorted quantified modal logic we call the Formula of the Universal Law Logic (FULL). The FULL formalizes Kant's first formulation of the categorical imperative, the Formula of the Universal Law (FUL), and concepts such as causality and agency. We demonstrate on three cases from Kantian ethics that the FULL can reason to evaluate agents' actions for certain purposes without built-in moral intuition, given that it has sufficient (non-normative) background knowledge. Therefore, the FULL is a contribution towards more robust and autonomous AMAs, and a more formal understanding of Kantian ethics.