Concept Lattice Representations of Annotated Taxonomies

We show how the concept of an annotated ordered set can be used to model large taxonomically structured ontologies such as the Gene Ontology. By constructing a formal context consistent with a given annotated ordered set, their concept lattice representations are derived. We develop the fundamental mathematical relations present in this formulation, in particular deriving a conceptual pre-ordering of the taxonomy, and constructing a correspondence between the annotations of an ordered set and the closure systems of its filter lattice. We study an example from the Gene Ontology to demonstrate how the introduced technique can be utilized for ontology review.