Abstract We introduce a hybrid spatiotemporal logic for automotive safety applications (HSTL), focused on highway driving. Spatiotemporal logic features specifications about vehicles throughout space and time, while hybrid logic enables precise references to individual vehicles and their historical positions. We define the semantics of HSTL and provide a baseline model-checking algorithm for it. We propose two optimized model-checking algorithms, which reduce the search space based on the reachable states and possible transitions from one state to another. All three model-checking algorithms are evaluated on a series of common driving scenarios such as safe following, safe crossings, overtaking, and platooning. An exponential performance improvement is observed for the optimized algorithms.

Normative Restraining Bolts (NRBs) adapt the restraining bolt technique (originally developed for safe reinforcement learning) to ensure compliance with social, legal, and ethical norms. While effective, NRBs rely on trial-and-error weight tuning, which hinders their ability to enforce hierarchical norms; moreover, norm updates require retraining. In this paper, we reformulate learning with NRBs as a multi-objective reinforcement learning (MORL) problem, where each norm is treated as a distinct objective. This enables the introduction of Ordered Normative Restraining Bolts (ONRBs), which support algorithmic weight selection, prioritized norms, norm updates, and provide formal guarantees on minimizing norm violations. Case studies show that ONRBs offer a robust and principled foundation for RL-agents to comply with a wide range of norms while achieving their goals.

We modify the restraining bolt technique, originally designed for safe reinforcement learning, to regulate agent behavior in alignment with social, ethical, and legal norms. Rather than maximizing rewards for norm compliance, our approach minimizes penalties for norm violations. We demonstrate in case studies the effectiveness of our approach in capturing benchmark challenges in normative reasoning like contrary-to-duty obligations, exceptions, and temporal obligations.