{"ID":2829126,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.13670","arxiv_id":"2512.13670","title":"NL2SpaTiaL: Generating Geometric Spatio-Temporal Logic Specifications from Natural Language for Manipulation Tasks","abstract":"While Temporal Logic provides a rigorous verification framework for robotics, it typically operates on trajectory-level signals and does not natively represent the object-centric geometric relations that are central to manipulation. Spatio-Temporal Logic (SpaTiaL) overcomes this by explicitly capturing geometric spatial requirements, making it a natural formalism for manipulation-task verification. Consequently, translating natural language (NL) into verifiable SpaTiaL specifications is a critical objective. Yet, existing NL-to-Logic methods treat specifications as flat sequences, entangling nested temporal scopes with spatial relations and causing performance to degrade sharply under deep nesting. We propose NL2SpaTiaL, a framework modeling specifications as Hierarchical Logical Trees (HLT). By generating formulas as structured HLTs in a single shot, our approach decouples semantic parsing from syntactic rendering, aligning with human compositional spatial reasoning. To support this, we construct, to the best of our knowledge, the first NL-to-SpaTiaL dataset with explicit hierarchical supervision via a logic-first synthesis pipeline. Experiments with open-weight LLMs demonstrate that our HLT formulation significantly outperforms flat-generation baselines across various logical depths. These results show that explicit HLT structure is critical for scalable NL-to-SpaTiaL translation, ultimately enabling a rigorous ``generate-and-test'' paradigm for verifying candidate trajectories in language-conditioned robotics. Project website: https://sites.google.com/view/nl2spatial","short_abstract":"While Temporal Logic provides a rigorous verification framework for robotics, it typically operates on trajectory-level signals and does not natively represent the object-centric geometric relations that are central to manipulation. Spatio-Temporal Logic (SpaTiaL) overcomes this by explicitly capturing geometric spatia...","url_abs":"https://arxiv.org/abs/2512.13670","url_pdf":"https://arxiv.org/pdf/2512.13670v2","authors":"[\"Licheng Luo\",\"Kaier Liang\",\"Yu Xia\",\"Mingyu Cai\"]","published":"2025-12-15T18:56:34Z","proceeding":"cs.RO","tasks":"[\"cs.RO\"]","methods":"[\"Large Language Model\"]","project_urls":"[\"https://sites.google.com/view/nl2spatial\"]","has_code":false,"code_links":[{"ID":605932,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_id":2829126,"paper_url":"https://arxiv.org/abs/2512.13670","paper_title":"NL2SpaTiaL: Generating Geometric Spatio-Temporal Logic Specifications from Natural Language for Manipulation Tasks","repo_url":"https://github.com/google/safevalues","is_official":false,"mentioned_in_paper":false,"mentioned_in_github":true,"github_stars":0}]}