Abstract. Conceptual Information Systems unfold the conceptual structure of data stored in relational databases. In the design phase of the system, conceptual hierarchies have to be created which describe di erent aspects of the data. In this paper, we describe two principal ways of designing such conceptual hierarchies, data driven design and theory driven design,and discuss advantages and drawbacks. The central part of the paper shows how Attribute Exploration,a knowledge acquisition tool developed by B. Ganter can be applied for narrowing the gap between both approaches.