Structural-Ambiguity-Aware Translation from Natural Language to Signal Temporal Logic

Signal Temporal Logic (STL) is an expressive formal language for specifying spatio-temporal requirements over real-valued, real-time signals. It has been widely used for the verification and synthesis of autonomous systems and cyber-physical systems. In practice, however, users often express their requirements in natural language rather than in structured STL formulas, making natural-language-to-STL translation a critical yet challenging task. Manual specification requires temporal-logic expertise and cannot scale, while prompting commercial LLM APIs incurs substantial token costs and may expose sensitive system requirements to third-party services, raising privacy concerns for industrial deployment. To address these challenges, we present ReasonSTL, a tool-augmented framework that adapts local open-source language models for natural-language-to-STL generation. ReasonSTL decomposes the translation process into explicit reasoning, deterministic tool calls, and structured formula construction. We further introduce process-rewarded training to supervise both tool-use trajectories and final formulas, together with STL-Bench, a bilingual, computation-aware benchmark grounded in real-world signals. Experiments show that a 4B model trained with ReasonSTL achieves state-of-the-art performance in both automatic metrics and human evaluations, demonstrating that ReasonSTL provides a transparent, low-cost, and privacy-preserving alternative for formal specification drafting.

Signal Temporal Logic (STL) enables rigorous verification and control of cyber-physical systems, but writing correct specifications requires expertise that most requirement holders lack. Large language models can translate natural-language (NL) requirements into STL, yet stronger translators alone approach an accuracy ceiling. We argue that this ceiling stems from how the task is posed: one-shot, open-loop translation is somewhat ill-defined. Natural language is ambiguous, and, more fundamentally, what a person writes may not always be what they intend, so the target specification is not fully contained in the input text. We therefore reformulate NL-to-STL translation as a closed-loop feedback process. Each generated formula is translated back into natural language for the user to check, and natural-language corrections drive revision until the user accepts the specification. Users never read or write formal syntax. This framework rests on an asymmetry familiar from feedback control theory. The forward path, from ambiguous language to formal logic, is hard and error-prone. The feedback path, from structured STL back to language, can be made highly precise, and a precise feedback path lets an imprecise forward path achieve precise closed-loop behavior. Experiments on 500 expert-authored requirements and seven LLMs support this view. Back-translated explanations agree with expert judgments in 99.5% of cases. Closed-loop refinement raises strong models from about 89% open-loop accuracy to 98.0--99.2%, and yields gains of over 30 percentage points for weaker models (e.g., 17.6%$\rightarrow$48.0%). Ablations show these gains come from the semantic content of the feedback rather than from repeated attempts. An expert audit and a 280-session user study further confirm the reliability of the loop. We also identify a capability threshold above which feedback no longer helps.

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.