Neural-network-based AI systems, including large vision-language models, often recognise the entities in a diagram but struggle with the relations between them. Their apparent successes frequently rest on shortcuts learned from training data rather than genuine understanding. NADUR proposes a new paradigm of neurosymbolic AI grounded in embodied cognition. Instead of linking neural networks directly to predicate logic, it adds an intermediate level. At that level, qualitative representations of spatial perception are combined with image schemas through conceptual blending. Image schemas are the recurring patterns of bodily interaction that structure human understanding. The project will (1) develop a formal, computational theory of the image-schematic structure and dynamics underlying the understanding of diagrams; (2) implement a neurosymbolic system that takes an image of an abstract diagram, as used in mathematics and computer science, and produces an image-schematic interpretation; and (3) use this to support reasoning, abstraction and analogy-making in a way humans can more easily interpret. NADUR is a fundamental research project that contributes to more robust, explainable and human-centred AI.