A Model-Theoretic Framework for Theories of Syntax

A natural next step in the evolution of constraint-based grammar formalisms from rewriting formalisms is to abstract fully away from the details of the grammar mechanism---to express syntactic theories purely in terms of the properties of the class of structures they license. By focusing on the structural properties of languages rather than on mechanisms for generating or checking structures that exhibit those properties, this model-theoretic approach can offer simpler and significantly clearer expression of theories and can potentially provide a uniform formalization, allowing disparate theories to be compared on the basis of those properties. We discuss $\LKP$, a monadic second-order logical framework for such an approach to syntax that has the distinctive virtue of being superficially expressive---supporting direct statement of most linguistically significant syntactic properties---but having well-defined strong generative capacity---languages are definable in $\LKP$ iff they are strongly context-free. We draw examples from the realms of GPSG and GB.