An Algebraic Characterization of STUF

Abstract

Unification-based grammar formalisms rest on the representation of linguistic entities in terms of feature-value structures. Lexical entries, grammar rules, phrases, and sentences are represented by complex feature structures enriched with equality. Speaking of feature structures as linguistic types suggests to look at other areas where types have been studied for a long time: the world of abstract data type specifications. One immediately observes a number of similarities between feature types and data types. The major link is the concept of equality which plays a central role in both approaches. Taking this as the starting point, we employ the algebraic machinery known from abtract data type specifications to the Stuttgart Type Unification Formalism (STUF). STUF provides a powerful notation for handling feature graphs, and the algebraic characterization of STUF we present here contributes to the formal understanding of the formalism. By translating feature graphs into algebraic data type specifications we are able to define an algebraic semantics for feature graphs. The algebraic framework also provides simple and precise definitions of operations of STUF graphs such as unification, subsumption and equivalence. Moreover, by employing the Knuth-Bendix Algorithm, a well-known tool for normalizing systems of equations, the various consistency concepts used for feature graph descriptions can be described and tested easily.