“…We need a formal grounding for knowledge integration over distributed semantic hierarchies, and thus turn to the mathematics of hierarchy, that is order theory, or the theory of lattices and ordered sets (posets) [1,3]. Our research program [7,8,9,10,11,12,17,18] is built on the representation of taxonomic ontologies as ordered sets. This technology encompasses not only existing ontology analysis mechanisms such as semantic similarities [2,13], but also provides methods for ontology integration which are especially appropriate for the open-world modeling of semantic web services and SSWAP.…”