A Formal Model for Topic Maps

Topic maps have been developed in order to represent the structures of relationships between subjects, independently of resources documenting them, and to allow standard representation and interoperability of such structures. The ISO 13250 XTM specification [2] have provided a robust syntactic XML representation allowing processing and interchange of topic maps. But topic maps have so far suffered from a lack of formal description, or conceptual model. We propose here such a model, based on the mathematical notions of hypergraph and connexity. This model addresses the critical issue of topic map organization in semantic layers, and provides ways to check semantic consistency of topic maps. Moreover, it seems generic enough to be used as a foundation for other semantic standards, like RDF [3].