Relationeel Neurosymbolisch Sequentieel Redeneren

Developing intelligent agents that can operate reliably in uncertain and dynamic environments requires more than raw predictive power. These agents must be able to perceive the world from high-dimensional sensory data, such as images or text, sequentially reason over structured representations of their environment, make informed decisions under uncertainty, and generalise across novel tasks, objects, or contexts. While deep learning excels at pattern recognition from data, it struggles to incorporate prior knowledge, provide interpretability, or guarantee robustness outside the training distribution. On the other hand, symbolic reasoning offers structure and guarantees but lacks scalability and the ability to deal with raw perceptual inputs. This dissertation addresses these limitations by advancing neurosymbolic AI (NeSy) towards sequential decision making. We explore how to unify probabilistic reasoning, logical structure, and neural perception into cohesive models that can act, learn, and reason over time. The focus is on building agents that can combine subsymbolic perception with structured probabilistic models, handle partial or missing knowledge, and operate under logical constraints, all within a principled and differentiable framework. The first part of the dissertation introduces dynamic decision circuits (DDCs), a framework for planning under uncertainty using compiled arithmetic circuits derived from sequential probabilistic graphical models. These circuits represent sequential decision problems in a symbolic and algebraic form while allowing for efficient and differentiable inference. This enables agents to reason about future states and rewards, and to learn model parameters from data through gradient-based optimisation. This contribution demonstrates how knowledge compilation techniques can be extended to sequential settings, bridging the gap between model-based decision-making and deep learning. Next, we propose relational neurosymbolic Markov models (NeSy-MMs), a new class of differentiable models that combine neural perception, relational logic, and probabilistic reasoning in time-dependent domains. NeSy-MMs use neural modules to map raw inputs to symbolic representations, which are then processed by a probabilistic logical model that evolves over time. The system supports both generative and discriminative tasks, accommodates partially specified domain knowledge, and allows for the end-to-end learning of both neural and symbolic components via a differentiable particle filter. Logical constraints are enforced during inference, allowing for interpretability, formal guarantees, and strong generalisation across entity configurations. Finally, the third part of the dissertation investigates how neurosymbolic reasoning can be applied in online learning settings, such as reinforcement learning. We introduce a codebase that integrates probabilistic logic shields with deep RL agents in the MiniHack environment. These shields act as runtime guards, renormalising unsafe or undesirable actions based on symbolic constraints. This approach improves both safety and sample efficiency, while preserving compatibility with standard RL algorithms. A web-based platform showcases the resulting agents and allows broader access to neurosymbolic RL techniques. Collectively, these contributions offer building blocks for a new generation of AI systems that learn from data, reason under uncertainty, adapt to new situations, and provide structured, interpretable behaviour. They demonstrate how symbolic and subsymbolic methods can be effectively combined in sequential settings, and lay the groundwork for future AI agents that are robust, safe, and capable of principled generalisation.