Explainable Artificial Intelligence (AI) is key to achieving a human-centred and ethical development of digital and industrial solutions. ENEXA builds upon novel and promising results in knowledge representation and machine learning to develop scalable, transparent and explainable machine learning algorithms for knowledge graphs. The project focuses on knowledge graphs because of their critical role as enabler of new solutions across domains and industries in Europe. Some of the existing machine learning approaches for knowledge graphs are known to already provide guarantees with respect to their completeness and correctness. However, they are still impossible or impractical to deploy on real-world data due to the scale, incompleteness and inconsistency of knowledge graphs in the wild. We devise approaches that maintain formal guarantees pertaining to completeness and correctness while being able to exploit different representations of knowledge graphs in a concurrent fashion. With our new methods, we plan to achieve significant advances in the efficiency and scalability of machine learning, especially on knowledge graphs. A supplementary innovation of ENEXA lies in its approach to explainability. Here, we focus on devising human-centred explainability techniques based on the concept of co-construction, where human and machine enter a conversation to jointly produce human-understandable explanations. Three use cases on business software services, geospatial intelligence and data-driven brand communication have been chosen to apply and validate this new approach. Given their expected growth rates, these sectors will play a major role in future European data value chains.