TAILIEUCHUNG - Báo cáo khoa học: "A COMPLETE AND RECURSIVE FEATURE THEORY*"

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 firstorder theory F T 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. . | A COMPLETE AND RECURSIVE FEATURE THEORY Rolf Backofen and Gert Smolka German Research Center for Artificial Intelligence DFKI W-6600 Saarbrucken Germany backofen smolka @ Abstract 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. 1 Introduction Feature descriptions provide for the typically partial description of abstract objects by means of functional attributes called features. They originated in the late seventies with so-called unification grammars 14 a by now popular family of declarative grammar formalisms for the description and processing of natural language. More recently the use of feature descriptions in logic programming has been advocated and studied 2 3 4 17 16 . Essentially feature descriptions provide a logical version of records a data structure found in many programming languages. Feature descriptions have been proposed in various forms with various formalizations 1 13 9 15 5 10 . We will follow the logical approach pioneered by 15 which accommodates feature descriptions as standard first-order formulae interpreted in first-order structures. In this approach a semantics for We appreciate discussions with Joachim Niehren and Ralf Treinen who

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