Multi-dimensional Representations of Conceptual Hierarchies

Dealing with conceptual hierarchies is a fundamental task when working with conceptual structures. In this paper we present a projection of the implications underlying such a hierarchy into the ndimensional space. This vector representation of the structure allows more complex mathematical treatment of the conceptual hierarchy. A first implementation of this idea is an enhanced representation of concept lattices from Formal Concept Analysis (FCA). From this representation we generate two-dimensional diagrams that respect certain aspects of the underlying semantics. In addition, manipulation and general interaction with the diagram become much more intuitive to the user. The experience with this implementation shows that a well-founded representation of the conceptual hierarchy improves the usability of a system based on this hierarchy.