Knowledge systems technologies are dominated by graphical structures, including ontologies, semantic graph databases, and concept lattices. A critical but typically overlooked aspect of all of these structures is their admission to analyses in terms of formal hierarchical relations. Transitivities of network links necessarily result in hierarchical levels, whether explicitly within directed acyclic graphs (DAGs) or implicitly through the identification of cycles. And whether from transitive link types in semantic graphs, or the explicit lattice structures of Formal Concept Analysis, the partial order representations of whatever hierarchy is present within a knowledge structure afford opportunities to exploit these hierarchical constraints for a variety of tasks, including ontology analysis and alignment, visual layout, and anomaly detection. In this wrokshop paper we introduce the basic concepts involved and draw connections among these application areas. Our goal in this workshop paper is to introduce the impact of a hierarchical (order-theoretical) analysis on directed acyclic graphs in knowledge systems tasks.
Revised: August 1, 2012 |
Published: December 9, 2009