Ensuring responsible use of artificial intelligence (AI) has become imperative as autonomous systems increasingly influence critical societal domains. However, the concept of trustworthy AI remains broad and multi-faceted. This thesis advances knowledge in the safety, fairness, transparency, and accountability of AI systems. In safety, we extend classical deterministic shielding techniques to become resilient against delayed observations, enabling practical deployment in real-world conditions. We also implement both deterministic and probabilistic safety shields into simulated autonomous vehicles to prevent collisions with road users, validating the use of these techniques in realistic driving simulators. We introduce fairness shields, a novel post-processing approach to enforce group fairness in sequential decision-making settings over finite and periodic time horizons. By optimizing intervention costs while strictly ensuring fairness constraints, this method efficiently balances fairness with minimal interference. For transparency and accountability, we propose a formal framework for assessing intentional behaviour in probabilistic decision-making agents, introducing quantitative metrics of agency and intention quotient. We use these metrics to propose a retrospective analysis of intention, useful for determining responsibility when autonomous systems cause unintended harm. Finally, we unify these contributions through the ``reactive decision-making'' framework, providing a general formalization that consolidates previous approaches. Collectively, the advancements presented contribute practically to the realization of safer, fairer, and more accountable AI systems, laying the foundations for future research in trustworthy AI.

Currently, many verification algorithms are available to improve the reliability of software systems. Selecting the appropriate verification algorithm typically demands domain expertise and non-trivial manpower. An automated algorithm selector is thus desired. However, existing selectors, either depend on machine-learned strategies or manually designed heuristics, encounter issues such as reliance on high-quality samples with algorithm labels and limited scalability. In this paper, an automated algorithm selection approach, namely MFH, is proposed for software verification. Our approach leverages the heuristics that verifiers producing correct results typically implement certain appropriate algorithms, and the supported algorithms by these verifiers indirectly reflect which ones are potentially applicable. Specifically, MFH embeds the code property graph (CPG) of a semantic-preserving transformed program to enhance the robustness of the prediction model. Furthermore, our approach decomposes the selection task into the sub-tasks of predicting potentially applicable algorithms and matching the most appropriate verifiers. Additionally, MFH also introduces a feedback loop on incorrect predictions to improve model prediction accuracy. We evaluate MFH on 20 verifiers and over 15,000 verification tasks. Experimental results demonstrate the effectiveness of MFH, achieving a prediction accuracy of 91.47% even without ground truth algorithm labels provided during the training phase. Moreover, the prediction accuracy decreases only by 0.84% when introducing 10 new verifiers, indicating the strong scalability of the proposed approach.

When reasoning about actions, e.g., by means of task planning or agent programming with Golog, the robot's actions are typically modeled on an abstract level, where complex actions such as picking up an object are treated as atomic primitives with deterministic effects and preconditions that only depend on the current state. However, when executing such an action on a robot it can no longer be seen as a primitive. Instead, action execution is a complex task involving multiple steps with additional temporal preconditions and timing constraints. Furthermore, the action may be noisy, e.g., producing erroneous sensing results and not always having the desired effects. While these aspects are typically ignored in reasoning tasks, they need to be dealt with during execution. In this thesis, we propose several approaches towards closing this gap.

Formal methods refer to rigorous, mathematical approaches to system development and have played a key role in establishing the correctness of safety-critical systems. The main building blocks of formal methods are models and specifications, which are analogous to behaviors and requirements in system design and give us the means to verify and synthesize system behaviors with formal guarantees. This monograph provides a survey of the current state of the art on applications of formal methods in the autonomous systems domain. We consider correct-by-construction synthesis under various formulations, including closed systems, reactive, and probabilistic settings. Beyond synthesizing systems in known environments, we address the concept of uncertainty and bound the behavior of systems that employ learning using formal methods. Further, we examine the synthesis of systems with monitoring, a mitigation technique for ensuring that once a system deviates from expected behavior, it knows a way of returning to normalcy. We also show how to overcome some limitations of formal methods themselves with learning. We conclude with future directions for formal methods in reinforcement learning, uncertainty, privacy, explainability of formal methods, and regulation and certification.

In 2020, poor-quality software systems led to financial losses of approximately USD 2.08 trillion in the U.S. alone.19 Formal methods, such as bounded model checking (BMC), help to improve software quality, but they often fail to scale to the size and complexity of software.