Cost-effective semantic description and annotation of shared knowledge resources has always been of great importance for digital libraries and large scale information systems in general. With the emergence of the Social Web and Web 2.0 technologies, a more effective semantic description and annotation, e.g., folksonomies, of digital library contents is envisioned to take place in collaborative and personalised environments. However, there is a lack of foundation and mathematical rigour for coping with contextualised management and retrieval of semantic annotations throughout their evolution as well as diversity in users and user communities. In this paper, we propose an ontological foundation for semantic annotations of digital libraries in terms of flexonomies. The proposed theoretical model relies on a high dimensional space with algebraic operators for contextualised access of semantic tags and annotations. The set of the proposed algebraic operators, however, is an adaptation of the set theoretic operators
selection, projection, difference, intersection, union in database theory. To this extent, the proposed model is meant to lay the ontological foundation for a Digital
Library 2.0 project in terms of geometric spaces rather than logic (description) based formalisms as a more efficient and scalable solution to the semantic annotation
problem in large scale.