The upper bounds of Information Retrieval (IR) effectiveness could be improved if new frameworks were investigated beyond traditional retrieval models. Vector spaces and their untraditional operators – meet and join – are a step in this direction. On the other hand, users might express complex information needs. Complex information needs may take the form of themes, which cannot be effortlessly expressed using plain natural language queries. Therefore, new theoretical structures and operators should be designed for allowing users to express themes.

This paper illustrates how meet and join of vector spaces can rank documents by a relevance measure. Meet and join act on themes modeled as vector subspaces; for example, meet intersects two planes while join builds a plane from two lines. Since an operator applies to a pair of themes and results in another theme operators and theme models replace the traditional retrieval models. The experimental results show that this approach can compete with – it can retrieve relevant documents missed by – traditional retrieval models.