Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoning
Summary: arXiv:2603.29868v1 Announce Type: new
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:
- Pareto-optimal Set: STR can be interpreted as a Pareto-optimal set that characterizes all admissible spatiotemporal perturbations.
- Computational Feasibility: 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.
Key Contributions
- Introduction of the concept of spatiotemporal robustness (STR), which integrates both spatial and temporal dimensions of robustness.
- Development of a formal framework for STR as a multi-objective reasoning problem.
- Identification of robust semantics for STR that ensure sound approximations and computational efficiency.
- Creation of monitoring algorithms tailored for real-time evaluation of STR in dynamic environments.
Implications for Future Research
The findings presented in this paper have significant implications for various fields that rely on autonomous systems. As the demand for robust systems increases, the ability to effectively manage uncertainties in both space and time becomes critical. Our work opens avenues for further exploration in:
- Multi-agent systems where coordination and interaction are essential.
- Smart city applications, enhancing the management of urban infrastructures.
- Air traffic control systems that require high reliability under varying conditions.
In conclusion, the proposed framework for spatiotemporal robustness provides a novel and robust approach to ensuring the reliability of autonomous systems in uncertain environments, paving the way for advancements in multi-objective reasoning within temporal logic tasks.