# Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning

arXiv: https://arxiv.org/abs/2603.29868 · HTML: https://mlsanity.com/paper/2603.29868/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 69 references that are in the map.
- First posted on arXiv 28 Jan 2026.

## Builds on (most cited first, 29 of 29)

- [Do As I Can, Not As I Say: Grounding Language in Robotic Affordances](https://mlsanity.com/paper/2204.01691/) (2022)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Reinforcement Learning With Temporal Logic Rewards](https://mlsanity.com/paper/1612.03471/) (2016)
- [NL2TL: Transforming Natural Languages to Temporal Logics using Large Language Models](https://mlsanity.com/paper/2305.07766/) (2023)
- [Backpropagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods](https://mlsanity.com/paper/2008.00097/) (2020)
- [Sample-Efficient Safety Assurances using Conformal Prediction](https://mlsanity.com/paper/2109.14082/) (2021)
- [Robust Online Monitoring of Signal Temporal Logic](https://mlsanity.com/paper/1506.08234/) (2015)
- [Conformal Prediction for STL Runtime Verification](https://mlsanity.com/paper/2211.01539/) (2022)
- [On Robustness Metrics for Learning STL Tasks](https://mlsanity.com/paper/2003.06041/) (2020)
- [STyLuS*: A Temporal Logic Optimal Control Synthesis Algorithm for Large-Scale Multi-Robot Systems](https://mlsanity.com/paper/1809.08345/) (2018)
- [Robust Temporal Logic Model Predictive Control](https://mlsanity.com/paper/1511.00347/) (2015)
- [A Smooth Robustness Measure of Signal Temporal Logic for Symbolic Control](https://mlsanity.com/paper/2006.05239/) (2020)
- [Arithmetic-Geometric Mean Robustness for Control from Signal Temporal Logic Specifications](https://mlsanity.com/paper/1903.05186/) (2019)
- [Mining Parametric Temporal Logic Properties in Model Based Design for Cyber-Physical Systems](https://mlsanity.com/paper/1512.07956/) (2015)
- [Control from Signal Temporal Logic Specifications with Smooth Cumulative Quantitative Semantics](https://mlsanity.com/paper/1904.11611/) (2019)
- [On-Line Monitoring for Temporal Logic Robustness](https://mlsanity.com/paper/1408.0045/) (2014)
- [Conformal Quantitative Predictive Monitoring of STL Requirements for Stochastic Processes](https://mlsanity.com/paper/2211.02375/) (2022)
- [Time Robustness in MTL and Expressivity in Hybrid System Falsification (Extended Version)](https://mlsanity.com/paper/1505.06307/) (2015)
- [When to Trust AI: Advances and Challenges for Certification of Neural Networks](https://mlsanity.com/paper/2309.11196/) (2023)
- [An STL-based Approach to Resilient Control for Cyber-Physical Systems](https://mlsanity.com/paper/2211.02794/) (2022)
- [Time-Robust Control for STL Specifications](https://mlsanity.com/paper/2104.02677/) (2021)
- [Study of Signal Temporal Logic Robustness Metrics for Robotic Tasks Optimization](https://mlsanity.com/paper/2110.00339/) (2021)
- [Temporal Robustness of Stochastic Signals](https://mlsanity.com/paper/2202.02583/) (2022)
- [Synthesis of Temporally-Robust Policies for Signal Temporal Logic Tasks using Reinforcement Learning](https://mlsanity.com/paper/2312.05764/) (2023)
- [Time Series Learning using Monotonic Logical Properties](https://mlsanity.com/paper/1802.08924/) (2018)
- [Combined Left and Right Temporal Robustness for Control under STL Specifications](https://mlsanity.com/paper/2306.04936/) (2023)
- [Quantifying Conformance using the Skorokhod Metric (full version)](https://mlsanity.com/paper/1505.05832/) (2015)
- [Time-Robust Path Planning with Piece-Wise Linear Trajectory for Signal Temporal Logic Specifications](https://mlsanity.com/paper/2403.10735/) (2024)

## Built on by (most cited first, 1 of 1)

- [Runtime Monitoring of Perception-Based Autonomous Systems via Embedding Temporal Logic](https://mlsanity.com/paper/2605.12651/) (2026)

## Abstract (arXiv)

The reliability of autonomous systems depends on their robustness, i.e., their ability to meet their objectives under uncertainty. In this paper, we study spatiotemporal robustness of temporal logic specifications evaluated over discrete-time signals. Existing work has proposed robust semantics that capture not only Boolean satisfiability, but also the geometric distance from unsatisfiability, corresponding to admissible spatial perturbations of a given signal. In contrast, we propose spatiotemporal robustness (STR), which captures admissible spatial and temporal perturbations jointly. This notion is particularly informative for interacting systems, such as multi-agent robotics, smart cities, and air traffic control. We define STR as a multi-objective reasoning problem, formalized via a partial order over spatial and temporal perturbations. This perspective has two key advantages: (1) STR can be interpreted as a Pareto-optimal set that characterizes all admissible spatiotemporal perturbations, and (2) STR can be computed using tools from multi-objective optimization. To navigate computational challenges, we propose robust semantics for STR that are sound in the sense of suitably under-approximating STR while being computationally tractable. Finally, we present monitoring algorithms for STR using these robust semantics. To the best of our knowledge, this is the first work to deal with robustness across multiple dimensions via multi-objective reasoning.