In practice, the target sequence often follows certain model properties or patterns (e.g., reasonable ranges, consecutive changes, resource constraint, temporal correlations between multiple variables, existence, unusual cases, etc.). However,RNNs cannot guarantee their learned distributions satisfy these properties.

We propose Differentiable Temporal Logic (DTL), a model-agnostic framework that introduces temporal constraints to deep networks. DTL treats the outputs of a network as a truth assignment of a temporal logic formula, and computes a temporal logic loss reflecting the consistency between the output and the constraints.

We introduce a machine learning approach to model checking temporal logic, with application to formal hardware verification. Model checking answers the question of whether every execution of a given system satisfies a desired temporal logic specification. Unlike testing, model checking provides formal guarantees. Its application is expected standard in silicon design and the EDA industry has invested decades into the development of performant symbolic model checking algorithms. Our new approach combines machine learning and symbolic reasoning by using neural networks as formal proof certificates for linear temporal logic. We train our neural certificates from randomly generated executions of the system and we then symbolically check their validity using satisfiability solving which, upon the affirmative answer, establishes that the system provably satisfies the specification. We leverage the expressive power of neural networks to represent proof certificates as well as the fact that checking a certificate is much simpler than finding one. As a result, our machine learning procedure for model checking is entirely unsupervised, formally sound, and practically effective. We experimentally demonstrate that our method outperforms the state-of-the-art academic and commercial model checkers on a set of standard hardware designs written in SystemVerilog.

We present a novel, regulator-driven approach for post hoc safety evaluation of learning-based, black-box autonomous mobile robots, ensuring ongoing compliance with evolving, human-defined safety rules. In our iterative workflow, human safety requirements are translated by regulators into Signal Temporal Logic (STL) specifications. Rollout traces from the black-box model are externally verified for compliance, yielding quantitative safety metrics, Total Robustness Value (TRV) and Largest Robustness Value (LRV), which measure average and worst-case specification adherence. These metrics inform targeted retraining and iterative improvement by model designers. We apply our method across two different applications: a virtual driving scenario and an autonomous mobile robot navigating a complex environment, and observe statistically significant improvements across both scenarios. In the virtual driving scenario, we see a 177% increase in traces adhering to the simulation speed limit, a 1138% increase in traces minimizing off-road driving, and a 16% increase in traces successfully reaching the goal within the time limit. In the autonomous navigation scenario, there is a 300% increase in traces avoiding sharp turns, a 200% increase in traces reaching the goal within the time limit, and a 49% increase in traces minimizing time spent near obstacles. Finally, we validate our approach on a TurtleBot3 robot in the real world, and demonstrate improved obstacle navigation with safety buffers.

Abstract--Autonomous systems increasingly rely on human feedback to align their behavior, expressed as pairwise comparisons, rankings, or demonstrations. While existing methods can adapt behaviors, they often fail to guarantee safety in safety-critical domains. We propose a safety-guaranteed, optimal, and efficient approach to solve the learning problem from preferences, rankings, or demonstrations using Weighted Signal T emporal Logic (WSTL). WSTL learning problems, when implemented naively, lead to multi-linear constraints in the weights to be learned. By introducing structural pruning and log-transform procedures, we reduce the problem size and recast the problem as a Mixed-Integer Linear Program while preserving safety guarantees. Experiments on robotic navigation and real-world Formula 1 data demonstrate that the method effectively captures nuanced preferences and models complex task objectives. Autonomous systems are increasingly part of our daily lives, from driverless cars in urban navigation to household robots performing domestic chores. Since these systems operate closely alongside humans, learning from human feedback is a natural way to ensure their behaviors align with human desires.

Abstract--This survey provides an analysis of current methodologies integrating legal and logical specifications into the perception, prediction, and planning modules of automated driving systems. We systematically explore techniques ranging from logic-based frameworks to computational legal reasoning approaches, emphasizing their capability to ensure regulatory compliance and interpretability in dynamic and uncertain driving environments. A central finding is that significant challenges arise at the intersection of perceptual reliability, legal compliance, and decision-making justifiability. T o systematically analyze these challenges, we introduce a taxonomy categorizing existing approaches by their theoretical foundations, architectural implementations, and validation strategies. We particularly focus on methods that address perceptual uncertainty and incorporate explicit legal norms, facilitating decisions that are both technically robust and legally defensible. The review covers neural-symbolic integration methods for perception, logic-driven rule representation, and norm-aware prediction strategies, all contributing toward transparent and accountable autonomous vehicle operation. We highlight critical open questions and practical trade-offs that must be addressed, offering multidisci-plinary insights from engineering, logic, and law to guide future developments in legally compliant autonomous driving systems.

We present Sentinel, the first framework for formally evaluating the physical safety of Large Language Model(LLM-based) embodied agents across the semantic, plan, and trajectory levels. Unlike prior methods that rely on heuristic rules or subjective LLM judgments, Sentinel grounds practical safety requirements in formal temporal logic (TL) semantics that can precisely specify state invariants, temporal dependencies, and timing constraints. It then employs a multi-level verification pipeline where (i) at the semantic level, intuitive natural language safety requirements are formalized into TL formulas and the LLM agent's understanding of these requirements is probed for alignment with the TL formulas; (ii) at the plan level, high-level action plans and subgoals generated by the LLM agent are verified against the TL formulas to detect unsafe plans before execution; and (iii) at the trajectory level, multiple execution trajectories are merged into a computation tree and efficiently verified against physically-detailed TL specifications for a final safety check. We apply Sentinel in VirtualHome and ALFRED, and formally evaluate multiple LLM-based embodied agents against diverse safety requirements. Our experiments show that by grounding physical safety in temporal logic and applying verification methods across multiple levels, Sentinel provides a rigorous foundation for systematically evaluating LLM-based embodied agents in physical environments, exposing safety violations overlooked by previous methods and offering insights into their failure modes.

Strategy logic (SL) is a powerful temporal logic that enables first-class reasoning over strategic behavior in multi-agent systems (MAS). In many MASs, the agents (and their strategies) cannot observe the global state of the system, leading to many extensions of SL centered around imperfect information, such as strategy logic with imperfect information (SL$_\mathit{ii}$). Along orthogonal lines, researchers have studied the combination of strategic behavior and hyperproperties. Hyperproperties are system properties that relate multiple executions in a system and commonly arise when specifying security policies. Hyper Strategy Logic (HyperSL) is a temporal logic that combines quantification over strategies with the ability to express hyperproperties on the executions of different strategy profiles. In this paper, we study the relation between SL$_\mathit{ii}$ and HyperSL. Our main result is that both logics (restricted to formulas where no state formulas are nested within path formulas) are equivalent in the sense that we can encode SL$_\mathit{ii}$ instances into HyperSL instances and vice versa. For the former direction, we build on the well-known observation that imperfect information is a hyperproperty. For the latter direction, we construct a self-composition of MASs and show how we can simulate hyperproperties using imperfect information.

This paper presents a temporal expression language for monitoring AI agent behavior, enabling systematic error-detection of LLM-based agentic systems that exhibit variable outputs due to stochastic generation processes. Drawing from temporal logic techniques used in hardware verification, this approach monitors execution traces of agent tool calls and state transitions to detect deviations from expected behavioral patterns. Current error-detection approaches rely primarily on text matching of inputs and outputs, which proves fragile due to the natural language variability inherent in LLM responses. The proposed method instead focuses on the sequence of agent actions -- such as tool invocations and inter-agent communications -- allowing verification of system behavior independent of specific textual outputs. The temporal expression language provides assertions that capture correct behavioral patterns across multiple execution scenarios. These assertions serve dual purposes: validating prompt engineering and guardrail effectiveness during development, and providing regression testing when agents are updated with new LLMs or modified logic. The approach is demonstrated using a three-agent system, where agents coordinate to solve multi-step reasoning tasks. When powered by large, capable models, all temporal assertions were satisfied across many test runs. However, when smaller models were substituted in two of the three agents, executions violated behavioral assertions, primarily due to improper tool sequencing and failed coordination handoffs. The temporal expressions successfully flagged these anomalies, demonstrating the method's effectiveness for detecting behavioral regressions in production agentic systems. This approach provides a foundation for systematic monitoring of AI agent reliability as these systems become increasingly deployed in critical applications.

This paper presents the initial results from our structured literature review on applications of Formal Methods (FM) to Robotic Autonomous Systems (RAS). We describe our structured survey methodology; including database selection and associated search strings, search filters and collaborative review of identified papers. We categorise and enumerate the FM approaches and formalisms that have been used for specification and verification of RAS. We investigate FM in the context of sub-symbolic AI-enabled RAS and examine the evolution of how FM is used over time in this field. This work complements a pre-existing survey in this area and we examine how this research area has matured over time. Specifically, our survey demonstrates that some trends have persisted as observed in a previous survey. Additionally, it recognized new trends that were not considered previously including a noticeable increase in adopting Formal Synthesis approaches as well as Probabilistic Verification Techniques.