A complete and recursive feature theory
Rolf Backofen, Gert Smolka · 1993
Various feature descriptions are being employed in constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions considered in this paper are the possibly quantified first-order formulae obtained from a signature of features and sorts. We establish a complete first-order theory FT by means of three axiom schemes and construct three elementarily equivalent models.One of the models consists of so-called feature graphs, a data structure common in computational linguistics. The other two models consist of so-called feature trees, a record-like data structure generalizing the trees corresponding to first-order terms.Our completeness proof exhibits a terminating simplification system deciding validity and satisfiability of possibly quantified feature descriptions.