Explainable artificial intelligence is a set of tools and processes that allows humans to understand and interpret predictions made by machine learning models. Knowledge graphs, together with artificial intelligence, can improve the accuracy and trustworthiness of the model outcomes. However, current knowledge graphs are limited in their ability to map complex, interconnected data at scale. Building upon recent advances in knowledge representation and artificial intelligence, the EU-funded ENEXA project will develop scalable, transparent and explainable machine learning algorithms for knowledge graphs. The focus will be placed on devising human-centred explainability techniques based on co-construction, where humans and machines initiate a conversation to jointly produce human-understandable explanations. To validate the proposed approaches, researchers will cover three use cases: business software services, geospatial intelligence and data-driven brand communications.