Competence-based extensions of Knowledge Space Theory are suggested as a formal framework for implementing key features of personalised learning in technology-enhanced learning. The approach links learning objects and assessment problems to the relevant skills that are taught or required. Various ways to derive these skills from domain ontologies are discussed in detail. Moreover, it is shown that the approach induces structures on the assessment problems and learning objects, respectively, that can serve as a basis for an efficient adaptive assessment of the learners' skills, and for selecting personalised learning paths. (Contains 6 figures.)