PaperlayerView exact revision on arXiv

Source-linked AI summary

Linear Temporal Logic Translation via Human-Inspired Self-Constrained Reasoning for Robot Task Specification

Haofei Hou, Fanxu Meng, Shunyi Zhao, Kairui Yang, Mengchen Cai, Lecheng Ruan, Qining Wang

arXiv:2608.28435v1cs.RO

TL;DR

Robotic task instructions are ambiguous natural-language descriptions that must be translated into precise, executable LTL specifications despite competing demands for formal constraint satisfaction and generalization. SCR internalizes structural knowledge through LTL-SCFG and hierarchical decision-making, guiding reinforcement-learning translation within a valid formal space. Experiments report consistent improvements over constrained and unconstrained baselines across constraint satisfaction, generalization, safety violation reduction, and interpretability.

  • Problem

    NL-to-LTL translation must satisfy strict syntactic and semantic domain constraints while generalizing to out-of-distribution instructions and novel task compositions.

  • Method

    SCR combines an LTL-SCFG constraint representation with hierarchical decision-making so structural knowledge guides translation throughout generation.

  • Results

    SCR consistently outperforms constrained and unconstrained baselines in domain-constraint satisfaction, generalization, safety violation reduction, and interpretability.

  • Takeaways & Limitations

    Internalizing structural knowledge enables translation within a formally grounded space while preserving adaptability to unseen instructions.

  • Takeaways & Limitations

    Existing approaches remain limited by post-hoc or external constraint intervention and by linear reasoning that makes intermediate logic difficult to regulate.

Abstract

from arXiv · show

Many robotic tasks are temporally extended and demand precise specifications of subgoals, constraints, and their temporal ordering. Yet human operators typically communicate such tasks in natural language, which is inherently ambiguous, underspecified, and context dependent. Translating human instructions into formal task specifications, such as Linear Temporal Logic (LTL), is therefore essential for verifiable and safe robotic execution. Existing LLM-based translators attempt to bridge this gap through open-ended reasoning or post-hoc constraint enforcement, but the former may violate domain constraints, whereas the latter can disrupt the reasoning needed for novel instructions. This paper proposes Self-Constrained Reasoning (SCR), a framework that mitigates this trade-off by internalizing structural knowledge into the model's decision-making process rather than imposing it as an external filter. By combining a structural constraint representation with a hierarchical decision-making formulation, SCR guides reasoning within a formally grounded space while preserving adaptability to unseen instructions. Experiments show that SCR improves both domain-constraint satisfaction and generalization, providing an effective and interpretable approach for translating human intent into verifiable specifications for robotic execution.

Introduction

Robots need precise formal specifications for temporally extended human tasks, but NL-to-LTL translation must simultaneously satisfy domain constraints and generalize to novel instructions. SCR addresses this tension by internalizing structural knowledge and guiding hierarchical reasoning within a valid formal space.

  • Motivation: Temporally extended robotic tasks combine ordered subgoals and safety constraints, making precise specifications important for safe execution.LTL specifications can support correct-by-construction controller or motion-plan synthesis.
  • Challenges: NL-to-LTL translation requires syntactic and semantic domain conformance while handling out-of-distribution instructions and novel task compositions.Generated formulas must follow LTL operator grammar, respect action semantics, and remain executable in robotic environments.
  • Existing Approaches: Constraint-guided methods improve formal correctness but can interfere with reasoning, whereas reasoning-enhanced methods improve generalization while overlooking domain constraints.Hybrid approaches partially mitigate this trade-off but generally rely on post-hoc correction or external intervention.
  • Limitations: External filters may correct syntax without resolving semantic inconsistencies, and linear reasoning makes intermediate logic difficult to regulate without restricting expressiveness.Unregulated latent reasoning can neglect input constraints and produce semantically inconsistent or unsafe actions.
  • Proposed Framework: SCR internalizes structural constraints during training and treats specification generation as hierarchical planning with domain-valid intermediate constructs.The framework aims to reduce syntactic and semantic errors while mapping unseen human intent to verifiable robotic specifications.
  • Contributions: Experiments report that SCR outperforms constrained and unconstrained baselines in domain-constraint satisfaction, generalization, safety violation reduction, and interpretability.The reported evaluation covers multiple properties of NL-to-LTL translation rather than a single performance dimension.

Methodology

The methodology represents LTL formulas with a recursive grammar and uses human-inspired hierarchical reasoning to translate NL instructions. LTL-SCFG constrains reinforcement-learning decisions while preserving source-language task decomposition.

  • Preliminaries: LTL specifies trajectory properties for discrete-time robotic systems whose dynamics are modeled as x_t+1 = f(x_t, u_t).The control objective is to synthesize a policy satisfying a task specification derived from an NL instruction.
  • Preliminaries: The LTL specification language uses a recursive prefix grammar containing atomic propositions, Boolean operators, and temporal operators.The grammar includes negation, conjunction, disjunction, globally, eventually, and until.
  • Preliminaries: Atomic propositions denote constrained state-space regions, while G, F, and U express global, eventual, and until conditions.An atomic proposition holds when its constraint function satisfies g_i(x) ≤ 0.
  • Cognitive Foundations and Overview of the Framework: SCR models translation as hierarchical reasoning governed by internalized structural rules inspired by human language production.The framework decomposes complex instructions into atomic propositions and nested temporal-logic subgoals.
  • Cognitive Foundations and Overview of the Framework: The framework uses a closed-loop hierarchical planning architecture to bound reasoning by LTL grammar while retaining flexibility lost under post-hoc filtering.This design is intended to prevent hallucinations associated with unconstrained reasoning models.
  • LTL-SCFG Constraint Extraction: LTL-SCFG is extracted from parallel instruction-formula corpora and used to constrain the RL agent’s action space during hierarchical translation.The pipeline combines grammar extraction, source-language task decomposition, and constrained decision-making.
  • LTL-SCFG Constraint Extraction: The LTL-SCFG tuple maps target-side operators to weighted source-side realizations, making the outermost operator or primitive the RL decision target.Source-side expressions support task decomposition while target-side structure constrains exploration.

LTL-SCFG Constraint Extraction

LTL-SCFG represents LTL translation with synchronized source–target grammar rules and uses the LTL syntax tree to align phrases, extract rules, and constrain translation decisions.

  • LTL-SCFG Definition: LTL-SCFG synchronizes English source expressions with LTL target expressions through production rules containing source and target terminal or nonterminal sequences.The source language is English, while the target language is LTL; shared nonterminals preserve correspondence between representations.
  • LTL-SCFG Definition: LTL-SCFG maps each target-side operator or atomic proposition to weighted source-side realizations, constraining the decision space while supporting task decomposition.The target vocabulary includes P and the operators ¬, ∧, ∨, G, F, and U.
  • Extraction Procedure: The extraction pipeline first identifies word alignments between LTL operators or atomic propositions and textual elements, then extracts hierarchical phrase-pair rules.The resulting rules are recursively composed and merged by target-side operator across domains.
  • Alignment Optimization: The method combines character, word-level, key-term, and sentence-level similarity components to optimize alignment beyond direct local similarity.The weighting factors γ_i balance the contributions of the four similarity measures.
  • Extracted Rules: Figure 3 visualizes extracted grammar rules across CleanUp, Drone, and Pick domains, showing how natural-language phrases map to LTL operators and atomic propositions.The figure’s tables compare formal operators such as F, G, and ¬ with their lexical realizations in different datasets.
  • Extraction Procedure: Grammar rules are derived recursively from nodes in the LTL syntax tree, with each node associated with the natural-language phrase corresponding to its subformula.The method assumes target expressions contain at most one operator and use nonterminal operands, enabling recursive composition.

Hierarchical Decision-Making Translation

The framework models NL-to-LTL translation as hierarchical, sequential decision-making constrained by LTL-SCFG rules. It separates operator selection from subtask decomposition and trains the decision agent with reinforcement learning and teacher forcing.

  • MDP Formulation: Translation is formulated as an MDP in which the agent selects an outermost LTL operator or atomic proposition and applies an LTL-SCFG rule to branch into subtasks.States encode syntax-tree nodes and generated text, while actions encode operator choices and resulting sub-sentences.
  • Reinforcement Learning Training: The translation objective is equivalent to the MDP optimization objective, supporting a top-down tree-structured translation process.The return recursion establishes equivalence between timestep-based rewards and the translation model objective.
  • Hierarchical Decision-Making: The action-selection module restricts choices to valid LTL-SCFG operators, narrowing the RL exploration space and focusing decisions on meaningful actions.The policy π1 is trained with a frozen BERT text encoder and additional contextual features.
  • Subtask Decomposition: Split execution then decomposes each translation into smaller subtasks using a BERT segmenter and grammar-guided structural alignment.Candidate segment boundaries divide sentences into three parts and are scored against canonical back-translations.
  • Subtask Decomposition: The segmentation probability combines neural and grammar-based components as PSeg = η1PBert + η2PScfg to balance domain performance and generalization.The grammar component scores syntactic alignment between segmented spans and SCFG rule components.
  • Reinforcement Learning Training: PPO optimizes the constrained decision policy by maximizing expected cumulative reward, with fixed rewards assigned for correct primitive selections.Teacher forcing samples subtrees as initial states and supervises local decisions with corresponding ground-truth English sentences.

Dataset

The evaluation uses three domain-specific datasets containing natural-language instructions, permissible atomic propositions, and target LTL formulas. It tests both in-distribution domain-constraint satisfaction and zero-shot generalization to withheld formulas.

  • Public Datasets: Each dataset contains triplets of NL instructions, permissible atomic propositions, and corresponding target LTL formulas.The datasets span diverse application domains for evaluating heterogeneous task contexts.
  • Public Datasets: Three datasets cover Drone Navigation, CleanUp, and Pick-and-Place tasks with 343, 39, and 5 distinct LTL formulas, respectively.Each dataset uses a 4:1 training-to-testing split for domain-constraint evaluation.
  • Zero-Shot Generalization: The zero-shot benchmark withholds target formulas during training, requiring translation of instructions into previously unseen formal specifications.Generalization sets contain 51 Drone Navigation formulas, 49 CleanUp formulas, and 3 Pick-and-Place formulas.

Baselines

The study compares SCR with baselines spanning soft knowledge injection, hard decoding constraints, reasoning enhancement, and traditional sequence or symbolic models. Figure 4 illustrates SCR’s recursive translation traces for CleanUp and Drone tasks.

  • LLM Baselines: Baseline LLMs are grouped into knowledge injection, decoding guidance, and reasoning and exploration enhancement methods.These categories distinguish soft constraints, hard constraints, and methods intended to improve reasoning or generalization.
  • LLM Baselines: Knowledge-injection baselines use retrieval-augmented generation or domain fine-tuning to provide task-specific information.The LLM-RAG configuration selects shot number by grid search, while fine-tuned models use domain data.
  • LLM Baselines: Decoding-guidance baselines enforce structural or lexical validity during generation through grammar-constrained decoding.Grammar-Constrained Decoding is implemented with the Guidance framework.
  • LLM Baselines: Reasoning-enhancement baselines include chain-of-thought models and RL-based models trained with sparse rewards for entirely correct translations.The comparisons also include RNN, CopyNet, BERT, and BERT-based E-NL2LTL traditional models.
  • Recursive Translation Showcases: Figure 4 shows CleanUp and Drone translations as recursive operator-selection and instruction-decomposition traces.The diagrams present the derivation step by step, emphasizing structured interpretability.

Training and Evaluation Settings

Evaluation measures exact translation and interpretable-model qualities, using domain-constraint and generalization test sets alongside human ratings. Experiments also include ablations and specify participant, hardware, and training settings.

  • Evaluation Metrics: Exact Match is the primary metric for both domain-constraint satisfaction and generalization because robot-executable translations must be fully accurate.The two capabilities are evaluated on separate test sets using EM.
  • Human Evaluation: Human evaluation measures Comprehensibility, Trust, Transparency, Fidelity, Interactivity, and Decision support.The final score averages ratings across all six dimensions.
  • Human Evaluation: The behavioral study used randomized examples from three scenarios and 9-point Likert ratings with 12 participants.Ratings ranged from strongly disagree at 1 to strongly agree at 9, with 5 as neutral.
  • Ablation Studies: Ablations remove the proposed constraint-extraction algorithm and compare Hiero-based extraction, unconstrained models, statistical translation, and action-classifier variants.These comparisons examine both extraction and reinforcement-learning contributions.
  • Implementation Settings: Public-dataset constraint extraction weights emphasize the segmenter with η1 = 0.75 and η2 = 0.25, while generalization testing reverses these weights.The weighting changes the relative contribution of neural segmentation and grammar-based rules.
  • Implementation Settings: Most experiments ran on one NVIDIA RTX 3090 GPU with batch size 128, 3 × 10^6 time steps, and learning rate 1 × 10^-5.The action and segmentation modules use MLP and BERT-based components, respectively.

Experiment Results

Across Drone Navigation, CleanUp, and Pick-and-Place, SCR achieves the strongest domain-constraint satisfaction while contrasting with methods that trade constraint adherence against reasoning or generalization.

  • Evaluation setup: The evaluation compares SCR with state-of-the-art methods across Drone Navigation, CleanUp, and Pick-and-Place using EM for domain constraint satisfaction.Table 1 summarizes the baseline comparison.
  • Overall performance: 94.66%, 98.82%, and 97.30% constraint satisfaction rates make SCR the best-performing framework across the three benchmarks.SCR outperforms fine-tuned Llama-3-8B and E-NL2LTL.
  • REM and GCD: GPT-5’s Drone score drops from 88.44% to 73.65% when CoT is introduced, while Llama-3-8B’s Pick score rises from 34.46% to 70.95% with GCD.The results illustrate opposing effects of reasoning enhancement and constrained decoding on domain satisfaction.
  • Fine-tuned Models and REM vs. GCD: Llama-3-8B falls from 91.59% to 86.90% in Drone with unconstrained RL, whereas GCD improves constraint adherence in fine-tuned models.The comparison indicates that optimization strategy affects whether fine-tuning preserves grammatical correctness.
  • Specialized and statistical models: E-NL2LTL reaches 97.78% in CleanUp, while Hiero remains around 30%, highlighting the gap between explicit structural constraints and purely statistical translation.Encoder-based models maintain robust performance, particularly in CleanUp.

Ablation Study

Ablations show that internalized structural constraints and hierarchical translation are central to SCR’s performance, while passive constraint enforcement and unconstrained reasoning expose trade-offs in generalization and safety.

  • Impact of LTL-SCFG: Removing LTL-SCFG lowers Drone performance from 94.66% to 87.15%, showing the importance of internalized constraints for structural grounding.Without LTL-SCFG, the system returns to a standard translation process lacking structural grounding.
  • Importance of Hierarchical Translation Modeling: Disabling hierarchical translation reduces Pick-and-Place accuracy from 97.30% to 89.19%, reflecting difficulty maintaining long-range temporal dependencies and ordering relations.The degradation exceeds eight percentage points under flat token generation.
  • Generalization Evaluation: RAG+GCD lowers Qwen-3-7B’s Cleanup generalization from 14.29% to 4.08%, whereas CoT raises GPT-5’s Pick accuracy from 38.30% to 68.09%.GCD improves domain satisfaction but can hamper unseen-formula generalization, while REM techniques show gains on held-out instructions.
  • Synergy of Self-Constrained Reasoning: SCR achieves generalization scores of 54.90%, 48.98%, and 74.47% across the three domains while keeping exploration within valid LTL syntax.Its structural knowledge is internalized rather than applied as a rigid external filter.
  • Safety Violation Evaluation: GPT-5-thinking reaches a 31.93 PF rate in Drone, while SCR records zero PFs and UA rates as low as 0.30% in Cleanup and 2.03% in Pick.The safety analysis distinguishes parsing failures from unintended actions.

Interpretability Evaluation

Human evaluation finds SCR strongest across all evaluated domains, with gains over GPT-5+CoT and a cognitive profile emphasizing comprehensibility and trust.

  • Human evaluation: SCR achieves average human-evaluation scores of 7.15 in Drone, 7.61 in CleanUp, and 6.39 in Pick.Participants rated generated specifications on a 1–9 Likert scale across six dimensions.
  • Interpretability dimensions: Radar charts compare SCR with baselines across Comprehensibility, Trust, Transparency, Fidelity, Interactivity, and Decision-support.The study uses these six qualitative metrics for multi-dimensional interpretability analysis.
  • Baseline comparison: SCR outperforms GPT-5+CoT by 0.12 to 1.01 points, with statistically significant improvements in CleanUp and Pick.The comparison concerns the strongest reasoning-based baseline.
  • Interpretability analysis: Hierarchical decomposition and internalized LTL-SCFG provide clearer decision support and reduce execution exceptions compared with end-to-end models.The paper presents these properties as aligning more effectively with human mental models.
  • Scope of interpretability gains: SCR’s advantages become more critical as task complexity increases, while Hiero is limited by its smaller primitive-formula set and structural depth.The paper specifically emphasizes transparency and formal correctness in Drone and CleanUp.

Application Experiments

The framework is evaluated across room cleaning, cargo delivery, manipulation, and household tasks, translating natural-language instructions into executable plans that satisfy logical constraints.

  • Experimental Scope: The experiments cover wheeled, humanoid, and dexterous-robot settings, with each experiment repeated at least three times and achieving a 100% success rate.The software runs on Ubuntu 20.04 and ROS Noetic with a remote host equipped with an Intel Xeon Gold 5218 CPU and 128 GB memory.
  • Room Cleaning: The room-cleaning environment models four colored rooms and requires transitions between rooms to pass through the floor area.The labeled finite transition system starts from the floor and labels room states with their corresponding colors.
  • Room Cleaning: In room cleaning, the robot enters the blue room at 3.0s and reaches the green-room objective at 9.3s.The plan is obtained by searching the synchronous product of the system and verification automata.
  • Cargo Delivery: In cargo delivery, the humanoid robot chooses waypoint K to satisfy G¬L1 before reaching landmark L2 at 30.0s.The execution begins at I, reaches K at 15.0s, and then proceeds to destination M associated with L2.
  • Manipulation: In manipulation, the robot picks the avocado, pear, and cucumber at 20.4s, 35.7s, and 61.9s, respectively, following a synchronous-product-derived plan.The avocado satisfies the ¬R constraint while maintaining logic state q1.
  • Household Experiment: In the household task, the virtual agent inserts and warms salmon before deactivating and closing the microwave at 8.33s.The agent activates the microwave at 3.40s, triggering a transition to q1, and generalizes to the task after fine-tuning.

Conclusion

The paper proposes SCR to integrate formal structural knowledge into hierarchical reasoning for natural-language-to-LTL translation. The framework is reported to improve constraint satisfaction, generalization, safety violation reduction, and interpretability.

  • Conclusion: SCR internalizes structural knowledge through hierarchical decision-making to balance reasoning flexibility with formal constraint satisfaction.Its LTL-SCFG representation and reinforcement-learning optimization guide exploration within a formally grounded space.
  • Conclusion: The framework integrates LTL-SCFG constraints with reinforcement learning to eliminate syntactic errors while enhancing generalization to out-of-distribution instructions.The approach differs from traditional post-hoc filtering by incorporating constraints into the reasoning process.
  • Conclusion: Experiments show consistent improvements over existing baselines in domain-constraint satisfaction, generalization, safety violation reduction, and interpretability.The reported pipeline transforms human intent into verifiable robotic behavior for complex, long-horizon tasks.
Loading 2608.28435v1…