This paper gives a data structure (UDS) for supporting database retrieval, inference and machine learning that attempts to unify and extend previous work in relational databases, semantic networks, conceptual graphs, RETE, neural networks and case-based reasoning. Foundational to this view is that all data can be viewed as a primitive set of objects and mathematical relations (as sets of tuples) over those objects. The data is stored in three partially-ordered hierarchies: a node hierarchy, a relation hierarchy, and a conceptual graphs hierarchy. All three hierarchies can be stored as \levels" in the conceptual graphs hierarchy. These multiplehierarchies support multipleviewsofthe datawithadvantagesover anyofthe individual methods. In particular, conceptual graphs are stored in a relation-based compact formthat facilitates matching. UDS is currently being implementedin the Peirce conceptual graphs workbench and is being used as a domain-independent monitorfor state-space search d...