Towards Trustworthy Legal AI through LLM Agents and Formal Reasoning

The rationality of law manifests in two forms: substantive rationality, which concerns the fairness or moral desirability of outcomes, and formal rationality, which requires legal decisions to follow explicitly stated, general, and logically coherent rules. Existing LLM-based systems excel at surface-level text analysis but lack the guarantees required for principled jurisprudence. We introduce L4M, a novel framework that combines adversarial LLM agents with SMT-solver-backed proofs to unite the interpretive flexibility of natural language with the rigor of symbolic verification. The pipeline consists of three phases: (1) Statute Formalization, where domain-specific prompts convert legal provisions into logical formulae; (2) Dual Fact and Statute Extraction, in which prosecutor- and defense-aligned LLMs independently map case narratives to fact tuples and statutes, ensuring role isolation; and (3) Solver-Centric Adjudication, where an autoformalizer compiles both parties' arguments into logic constraints, and unsat cores trigger iterative self-critique until a satisfiable formula is achieved, which is then verbalized by a Judge-LLM into a transparent verdict and optimized sentence. Experimental results on public benchmarks show that our system surpasses advanced LLMs including GPT-o4-mini, DeepSeek-V3, and Claude 4 as well as state-of-the-art Legal AI baselines, while providing rigorous and explainable symbolic justifications.