1 - Structures, Languages and Translations: the Structural Approach to Feature Logic

Abstract

This chapter reviews methodological issues involved in the structural approach used in feature logic. A direct consequence of the systematic approach to a variety of feature logics is that it clarifies the relationships between them. This is most explicit in the presentation of translations between various existing and putative feature logics which draws heavily on the correspondence theory that relates modal and classical languages. The chapter describes a general approach to the subject called the structural approach, and explains that thinking in structural terms is a useful way of thinking about unification formalisms and their interrelationships. At present, in contemporary unification-based linguistic frameworks, linguistic data is modelled by certain kinds of decorated labelled (directed) graphs. Perhaps the most prevalent way of thinking about unification-based grammar formalisms is that they are languages for expressing constraints on feature structures. Two basic ideas drive modal logic: one syntactic, and the other semantic. Modal languages are interpreted on Kripke models, which are set theoretic entities providing the following information. Propositional Dynamic Logic (PDL) is an extension of modal logic; PDL and some of its extensions are natural constraint languages for dealing with feature structures. Subsequently, Attribute Value Matrices (AVMs) are one of the most widely used methods of describing feature structures. A general setting for feature logic is the space of relational structures of model theory, together with the various languages for describing these structures, and the satisfiability preserving translations that exist among these languages. The basic ideas are very simple: feature structures are certain sorts of relational structures, and while there is a vast range of languages for talking about these structures, these languages are interrelated by satisfiability preserving translations.