Formally Verified Law as Reward Signal for Self-Improving Legal AI.

The article introduces a novel architecture designed to train legal AI by leveraging formally verifiable law as a reward signal. This approach adapts the "LLM proposes, verifier disposes" paradigm, typically seen in mathematical AI, to the unique demands of the legal domain. The proposed system comprises three key components: an LLM-driven autoformalization process that translates legal text into a formal legal calculus (extending Catala), a robust verification kernel, and an explanation generation module grounded in formal proof traces. For the computational aspects of law, this architecture offers provable correctness, ensuring that the AI's outputs are demonstrably accurate. For more open-textured legal analysis, it provides crucial structural guarantees: every necessary stage of a legal argument is addressed, argumentation is applied at the correct points, and the deductive links between steps are valid. The architecture's efficacy is demonstrated through applications to procedural deadline calculations in German law, Commerce Clause analysis in U.S. constitutional law, and cross-jurisdictional sanction proportionality. A significant advantage for legal AI training is that a deterministic external verifier supplies verifiable outcomes for legal problems, thereby closing the traditional reinforcement learning loop gap in legal applications.