Disjunctive Feature Structures As Hypergraphs

In this paper, we present a new mathematical framework in which disjunctive feature structures are defined as directed acyclic hypergraphs. Disjunction is defined in the feature structure domain, and not at the syntactic level in feature descriptions. This enables us to study properties and specify operations in terms of properties of, or operations on, hypergraphs rather than in syntactic terms. We illustrate the expressive power of this framework by defining a class of disjunctive feature structures with interesting properties (factored normal from or FNF), such as closure under factoring, unfactoring, unification, and generalization. Unification, in particular, has the intuitive appeal of preserving as much as possible the particular factoring of the disjunctive feature structures to be unified. We also show that unification in the FNF class can be extremely efficient in practical applications.