Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning

2026-01-28

AI Summary

This work addresses the challenge of quantifying robustness in autonomous systems subject to spatiotemporal disturbances, ensuring their compliance with temporal logic specifications under uncertainty. It introduces, for the first time, a notion of spatiotemporal robustness that jointly characterizes spatial and temporal perturbations, formalized as a Pareto-optimal set grounded in a partial order to uniformly capture multidimensional robustness. The approach integrates multi-objective optimization, robust semantics for temporal logic, and computable conservative approximations to devise an efficient monitoring algorithm. This algorithm achieves scalable computation while preserving semantic soundness, thereby enabling practical verification of system behavior in complex, uncertain environments.

Abstract

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.

Problem

• spatiotemporal robustness
• temporal logic
• robustness
• multi-objective reasoning
• uncertainty

Innovation

• spatiotemporal robustness
• temporal logic
• multi-objective reasoning
• Pareto optimality
• robust semantics