A complete and recursive feature theory

Abstract

Various feature descriptions are being employed in logic programming languages and constraint-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 binary and unary predicates called features and sorts, respectively. We establish a first-order theory FT by means of three axiom schemes, show its completeness, and construct three elementarily equivalent models.One of the models consists of the so-called feature graphs, a data structure common in computational linguistics. The other two models consist of the so-called feature trees, a recordlike 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.