The Formalization of WordNet by Methods of Relational Concept Analysis1

In this chapter a mathematical formalization of WordNet that relies on WordNet’s hierarchical and relational structure is described. Conceptual hierarchies are formalized in Formal Concept Analysis (Ganter & Wille, 1996), a theory developed at the Technische Hochschule Darmstadt over the last sixteen years (Section 7.2). This theory can be extended to Relational Concept Analysis by adding further relations (Section 7.4). In a linguistic application the conceptual hierarchies can be interpreted as hypernymy orderings, and other semantic relations such as meronymy and antonymy can be taken as additional relations. The theoretical analysis shows dependencies among semantic relations such as inheritance of relations from subconcepts to superconcepts. It does not provide a complete system of axioms for semantic relations, but it can facilitate the investigation of the logical properties of those relations. For example, it does not answer the question of whether meronymy is transitive in general, but it defines sufficient transitivity conditions to identify those properties that intransitive meronymy relations cannot have.