Syntax is more than you think

A number of statistical or grammatical models of natural language have been proposed over the years. All of them work a little bit; none of them work very well. It is easy to make them do something useful; it is extremely hard to make them do a lot more. This ease of initial success has led a number of people to make extravagant claims about computer processing of natural language. The difficulty of extending the success has led a number of people to make equally extravagant claims about what cannot be done with computing systems in natural language. We believe that much, much, more can be discovered through purely syntactic means (the only ones available to computers at present) than has been demonstrated. We also believe that syntax is not sufficient for any kind of understanding of natural language by computing systems, so that these syntactic studies must be augmented with some notion of semantics that relates the syntax to an interpretive context. This paper will describe some interesting and novel mathematical models that allow us to study the syntactic behavior of natural language to a much greater depth than usual, and show how they lead to some interesting experiments.