A hierarchical semantic net is a graph whose nodes represent concepts and whose links represent semantic hierarchical relationships, i.e., ones that satisfy the partial order property. Manually-built hierarchical semantic nets, such as thesauri, exist that support traditional information systems applications. The problem of automatically building and maintaining hierarchical semantic nets led us to explore the semantics of hierarchical relations. We argue that hierarchical relations between concepts imply—and depend on—consistent patterns in the way that concepts' properties relate to each other. Mathematically, these patterns—which we call regularity—are characterized by the fact that properties define graph homomorphisms from a hierarchy of concepts to graphs of property values for those concepts. Inheritance, which is used to characterize taxonomic (is-a) hierarchies, is a type of regularity. In this paper, we discuss the semantic implications of regularity and show instances of regularity for different hierarchical relations. In the same way that inheritance enables us to infer property values when those are not known, regularity enables us to infer property values through some sort of bidirectional inheritance—called expansion. However, to place a concept in a hierarchy based on its property values, we need an isomorphism between the hierarchy of concepts and the graphs of property values. Roughly speaking, such an isomorphism may be obtained by combining properties into a single mapping called description, and the corresponding relationship between descriptions is a combination of relations between property values—called context relation. In this paper, we describe the resulting Description-Context (DC) model of hierarchies, and a classification algorithm for DC hierarchies. Regularity, expansion, and classification were tested on two actual hierarchies built by librarians to support a biomedical bibliographic retrieval system. The results, which validated our models, are briefly described.