Traffic regulations are written for human interpretation and therefore rely on shared background knowledge and flexible phrasing, which inherently introduce ambiguity, context dependence, and semantic underspecification. These linguistic characteristics conflict with the precision required by computational reasoning engines such as Prolog, which demand explicit logical structure. This study evaluates two baseline translation approaches, Natural Language to Prolog (NL→Prolog) and Logical English to Prolog (LE→Prolog), and introduces a new reasoning-guided translation framework called Structured Four-Stage Legal Translation (S4L→Prolog). The proposed S4L framework performs semantic role extraction, scene completion, logical mapping, and Prolog rule generation within a single guided prompt, enabling direct translation of raw traffic rules into executable logic without human intervention. A benchmark consisting of twenty real-world traffic rules was used to evaluate each approach in terms of syntactic validity, semantic correctness, and logical completeness. S4L→Prolog achieves the highest accuracy, correctly formalizing 75 percent of the rules, while NL→Prolog reaches 60 percent and LE→Prolog reaches 55 percent. Qualitative analysis further shows that S4L captures implicit causal relations, deontic modality, and exception structure more reliably than the baselines. These results demonstrate that structured reasoning prompts can substantially improve the reliability of natural-language-to-logic translation for legal and safety-critical applications.
Neural machine translation (NMT) in the legal domain is a linguistically and conceptually demanding task, primarily due to the complexity of legal language and the high level of precision it requires. The recent emergence of reasoning-capable language models opens new possibilities for tackling such challenges. They add to a set of other previously proposed techniques to enhance the translation quality, which includes supervised fine-tuning and reinforcement learning. In this work, we perform a comparison between these various approaches. More particularly, we evaluate small language models such as Qwen3.5 4B, Qwen3.5 9B, and Gemma 3 12B enhanced with various re-training paradigms and compare their performances against frontier reasoning models. We focus on the Swiss legal system, which -- with its unique multilingual statutes -- offers a particularly challenging testbed for reasoning-augmented models. Our results show that the quality of small ``base'' models can be greatly enhanced, and that reinforcement learning with verifiable rewards can be applied to NMT in the legal domain and surpasses the translation quality of supervised fine-tuning. The performance of enhanced small models is close to the one of state-of-the-art reasoning models yet remains inferior. We also note that re-training paradigms yield diminishing returns as model size increase. The code and models are publicly available at https://github.com/aixiuxiuxiu/Legal-MT-SFT-RL.
Translating natural language instructions into machine-interpretable formal specifications enables robots and autonomous systems to plan, reason, and formally verify their behavior. However, existing translation models typically generate a specification for every input, even when the result is unreliable or fails to capture the user's intent, creating risks in safety-critical applications. Inspired by selective conformal prediction, we propose a selective translation framework that not only generates formal specifications but also determines when they can be trusted. Reliability is scored by two complementary black-box signals, the fidelity of the specification back-translated into natural language and the dispersion of repeated translations under exact semantic equivalence, which fail on different errors and jointly separate incorrect translations more sharply than either alone. Conformal risk control calibrates this score into a decision that accepts a specification or abstains, with a distribution-free bound on the rate at which incorrect specifications are accepted for execution, and a conformal anomaly detector on instruction embeddings screens out-of-distribution inputs before any translation is attempted. The proposed framework is general across formal specification languages, with experiments on Signal Temporal Logic (STL), Linear Temporal Logic (LTL), and geometric Spatio-Temporal Logic (SpaTiaL) demonstrating improved translation reliability, robustness under the evaluated cross-tier shifts, and effective uncertainty-aware abstention. This work establishes a foundation for trustworthy natural language interfaces by enabling AI systems to recognize when generated specifications may not be reliable.
Neurosymbolic reasoning has shown promising success in addressing complex reasoning tasks by combining large language models (LLMs) and symbolic solvers. While this approach shows promise, a fundamental challenge remains: improving the accuracy of translations from natural language to logical formulas. Current methods predominantly rely on prompt engineering, which is difficult to scale across different domains and input formats. Drawing inspiration from the success of fine-tuning in other model adaptation and alignment applications, we propose a fine-tuning-based Stratified Consistency Distillation approach: (1) We generate K logical translations per input using a frontier LLM and cluster them by semantic equivalence (2) Based on the entropy level, we apply majority voting (low entropy), LLM-as-a-Judge (medium entropy), or unification/abstention (high entropy), and (3) fine-tune a smaller model using the selected pseudo-labels. Our experiments show significant and consistent improvements in both Pass@K and our novel Equivalent Logical Similarity metrics, demonstrating the potential of advancing logical translation through consistency distillation.