pacSTL: PAC-Bounded Signal Temporal Logic from Data-Driven Reachability Analysis

2025-11-02

AI Summary

Formal safety verification of robotic systems under uncertainty remains challenging, as standard Signal Temporal Logic (STL) lacks native support for modeling stochastic uncertainty. Method: This paper introduces pacSTL, the first framework integrating Probably Approximately Correct (PAC) learning into STL. It constructs statistically guaranteed robustness measures at the atomic proposition level by combining PAC-bounded set prediction with interval-extended STL semantics, supported by data-driven reachability analysis, PAC boundary estimation, and interval optimization. Contribution/Results: pacSTL enables provably correct runtime safety monitoring. Evaluated on simulated and real-world autonomous small-vessel navigation tasks, it achieves high accuracy, strong robustness against distributional shifts, and favorable scalability. The framework establishes a novel paradigm for formal safety verification of uncertain cyber-physical systems, bridging statistical learning guarantees with temporal logic–based verification.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Natural Language Processing: Safety and Robustness
• Intelligent Robots: State Estimation

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Real-world robotic systems must comply with safety requirements in the presence of uncertainty. To define and measure requirement adherence, Signal Temporal Logic (STL) offers a mathematically rigorous and expressive language. However, standard STL cannot account for uncertainty. We address this problem by presenting pacSTL, a framework that combines Probably Approximately Correct (PAC) bounded set predictions with an interval extension of STL through optimization problems on the atomic proposition level. pacSTL provides PAC-bounded robustness intervals on the specification level that can be utilized in monitoring. We demonstrate the effectiveness of this approach through maritime navigation and analyze the efficiency and scalability of pacSTL through simulation and real-world experimentation on model vessels.

Problem

• Addressing uncertainty in robotic safety requirements
• Providing PAC-bounded robustness for temporal logic
• Enabling safety verification under uncertainty conditions

Innovation

• PAC-bounded set predictions for uncertainty handling
• Interval extension of Signal Temporal Logic
• Optimization problems on atomic proposition level