Bridging Legal Interpretation and Formal Logic: Faithfulness, Assumption, and the Future of AI Legal Reasoning
Authors: Olivia Peiyu Wang, Leilani H. Gilpin
Organizations: University of California, Santa Cruz
Abstract
The growing adoption of large language models in legal practice brings both significant promise and serious risk. Legal professionals stand to benefit from AI that can reason over contracts, draft documents, and analyze sources at scale, yet the high-stakes nature of legal work demands a level of rigor that current AI systems do not provide. The central problem is not simply that LLMs hallucinate facts and references; it is that they systematically draw inferences that go beyond what the source text actually supports, presenting assumption-laden conclusions as if they were logically grounded. This proposal presents a neuro-symbolic approach to legal AI that combines the expressive power of large language models with the rigor of formal verification, aiming to make AI-assisted legal reasoning both capable and trustworthy, thus reducing the burden of manual verification without sacrificing the accountability that legal practice demands.
Large Language Models (LLMs) achieve strong performance on reasoning tasks, but whether this reflects faithful logical inference or heuristic approximation remains unclear. We study this question in legal entailment by comparing three paradigms, including pure LLM classification, LLM-based Formal Reasoning, and solver-based Formal Reasoning using the Z3 SMT solver, on a re-annotated subset of ContractNLI across five LLMs. Our re-annotation reveals a systematic and measurable gap between pragmatic legal interpretation and strict formal entailment, where a substantial proportion of legally sound inferences are not formally grounded without additional unstated assumptions. While introducing formal structure improves accuracy, with LLM-based Formal Reasoning achieving the highest benchmark performance, we show that this gain does not imply faithful reasoning. We identify three recurring failure modes: scope laundering, where LLMs report solver-inconsistent classifications without executing the underlying formal reasoning, producing conclusions that appear logically grounded but are not; implicit constraint blindness, where LLMs overlook logical constraints present in formal representations; and program synthesis failures, where LLMs generate incorrect Z3 code despite structured prompting. Critically, scope laundering persists across all models, raising serious concerns about the faithfulness of LLM-based formal reasoning as a proxy for symbolic execution. These results reveal a fundamental gap between benchmark accuracy and logical faithfulness.
Recent advances in large language models (LLMs) have significantly enhanced automated legal reasoning. Yet, it remains unclear whether their performance reflects genuine legal reasoning ability or artifacts of data contamination. We present a comprehensive empirical study of tax law reasoning approaches and implement a contamination detection protocol to rigorously assess LLM reliability. We show that performance can be inflated by contamination. Building on this analysis, we conduct a systematic evaluation, comparing monolithic LLMs with hybrid systems that translate statutory text into formal representations and delegate inference to symbolic solvers. We build a novel test suite designed to probe generalization to unseen documents via case and rule variations. Our findings indicate that legal reasoning is inherently compositional and that neuro-symbolic frameworks offer a more reliable and robust foundation for legal AI, as well as improved generalization to unobserved situations.
Legal texts often contain computational legal clauses--provisions whose understanding requires complex logic. While frontier Large Reasoning Models (LRMs) can describe such clauses, building production-ready systems is limited by reasoning errors and the high cost of inference. We propose Amortized Intelligence, a neuro-symbolic approach where we use an LLM once to translate a legal text into Deterministic Autonomous Contract Language (DACL): a typed graph intermediate representation. Adjudication then relies on deterministic graph executions with a visually auditable trace. In comparison against runtime LRM baselines (including GPT-5.2 and Gemini 3 Pro), our DACL-based Agent achieves near-perfect consistency and mitigates the "reasoning cliff" observed in probabilistic models. The system reduces compute costs by over 90% in high-volume workflows while satisfying the strict auditability requirements of legal adjudication.