A Language Theoretic Approach to Syntactic Structure

We consider the idea of defining syntactic structure relative to a language, rather than to a grammar for a language. This allows us to define a notion of hierarchical structure that is independent of the particular grammar, and that depends rather on the properties of various algebraic structures canonically associated with a language. Our goal is not necessarily to recover the traditional ideas of syntactic structure invented by linguists, but rather to come up with an objective notion of syntactic structure that can be used for semantic interpretation. The role of syntactic structure is to bring together words and constituents that are apart on the surface, so they can be combined appropriately. The approach is based on identifying concatenation operations which are non-trivial and using these to constrain the allowable local trees in a structural description.