Draft What Does a Grammar Formalism Say about a Language?

Over the last ten or fteen years there has been a shift, in generative linguistics , away from formalisms based on a procedural interpretation of grammars towards constraint-based formalisms|formalisms that deene languages by specifying a set of constraints that characterize the set of well-formed structures analyzing the strings in the language. A natural extension of this trend is to deene this set of structures model-theoretically|to deene it as the set of mathematical structures that satisfy some set of logical axioms. This approach raises a number of questions about the nature of linguistic theories and the role of grammar formalisms in expressing them. In this paper we explore these questions and some of their consequences both for the model-theoretic and the grammar-based approaches to formalizing theories of syntax. With respect to the model-theoretic approach, we argue that linguistic theories cannot be captured simply by deening the set of structures licensed by a particular instance of a grammar. Rather, one must account for the generalizations the theory makes about language as well; one must capture the properties the theory ascribes to the natural languages as a class. With respect to grammar-based approaches, on the other hand, we argue that the actual meaning of the linguistic principles that are embodied in grammar formalisms is often times obscure. By reformulating these principles explicitly as properties of structures (or of classes of structures) one gains considerably clarity in understanding their consequences. We ground our discussion in a model-theoretic reinterpretation of Generalized Phrase-Structure Grammar. While there is little current active research on GPSG, it provides an ideal laboratory for exploring these issues. First, the formalism of GPSG is expressly intended to embody a great deal of the accompanying linguistic theory. Thus it provides a variety of opportunities for examining principles expressed as restrictions on the formalism from a model-theoretic point of view. At the same time, the fact that these restrictions embody universal grammar principles provides us with a variety of opportunities to explore the way in which the linguistic theory expressed by a grammar can transcend the mathematical theory of the structures it licenses. Finally, GPSG, DRAFT although deened declaratively, is a formalism with restricted generative capacity|a characteristic more typical of the earlier procedural formalisms. As such, one component of the theory it embodies is a claim about the language-theoretic complexity of natural languages. Such claims are diicult to establish for any of the constraint-based …