Know Your Limits : On the Faithfulness of LLMs as Solvers and Autoformalizers in Legal Reasoning
Authors: Olivia Peiyu Wang, Sanna Wong-Toropainen, Daneshvar Amrollahi, Ryan Bai, Tashvi Bansal, Arush Garg, Leilani H. Gilpin
Organizations: UC Santa Cruz · Univ. Helsinki · CodeX, Stanford · Stanford University · Canyon Crest Academy · Monta Vista High School · Los Altos High School
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.
Logical reasoning is essential for reliable AI, yet existing benchmarks are largely first-order-logic-centric, focusing on object-level deduction over fixed predicates. This misses many realistic scenarios where models must reason over rules, predicates, functions, constraints, and decision procedures themselves. We introduce HOLMES (Higher-Order Logic Meets real-world Explainable Symbolic reasoning), the first real-world benchmark for higher-order symbolic reasoning in LLMs, containing 1379 instances. Built on higher-order logic, HOLMES pairs natural-language problems with HOL formalizations, ground-truth answers, verifiable reasoning traces, and fine-grained controllable reasoning factors across law and finance. Experiments show that current LLMs still struggle on HOLMES, with an average accuracy of only 50.64% and the best model reaching 59.54%. Our analyses further reveal that high final-answer accuracy can mask shortcut reasoning in conflict-resolution settings, while performance drops sharply under scope-conditioned and compositional reasoning. These findings identify higher-order symbolic reasoning as a key bottleneck for building reliable and verifiable LLMs. The project code and dataset are publicly available at https://github.com/wuyucheng2002/HOLMES.
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.
Formalizing legal provisions promises machine-accessible law and automated legal reasoning, and recent LLMs make it tempting to generate such formalizations directly from statutory text. However, any formalization makes implicit interpretive choices whose consequences are hard to anticipate, especially if an LLM is the author. We present a method for systematically comparing different formalizations of the same legal provision by their inferences on individual cases. Given multiple formalizations of a provision, we match them at the node level, derive a shared interface for each pair from the matching, and use a SAT solver to enumerate the edge cases on which any two formalizations disagree. Selected edge cases are then verbalized into concrete factual scenarios that a legal expert can examine and act on. We apply our method to formalizations of ten EU provisions generated by nine frontier LLMs. We find that behavioral divergence between formalizations is essentially uncorrelated with their structural agreement and that the verbalized cases reveal qualitatively distinct types of disagreement, including divergences that mirror genuine controversies in the legal commentary.