On the Logic and Learning of Language (ePub)

Although certain publishers wouldn't believe it, this book is in part a foundational project in computational linguistics. The term "computational linguistics" is nowadays taken to refer to a kind of engineering discipline whose primary goal is to get computers to deal with information presented by means of ordinary language. This project exemplifies my view of computational linguistics, which is not as above. Consider for a moment what the various "computational sciences" amount to. Computational biology means using computer models to simulate biological systems and extract answers to questions of biology. Computational fluid dynamics (CFD) involves using computer models to simulate fluid dynamical systems and extract relevant answers—you get the idea. CFD is a favorite example because it is a relatively simple theory that has been plagued by a long history of computational obstacles.

The theory of CFD pretty much amounts to systems of equations that were first
derived in the nineteenth century, now called the Navier-Stokes equations. For
decades it has been thought, correctly, that if you want an answer to a fluid dynamical question, simply solve the Navier-Stokes equations. This last step proved to be very sticky since these equations can only be solved numerically (save a few special cases), and decades of work have been required to figure out decent methods for doing it; we are in some cases still waiting for sufficient computational power to get the answers we really want. In my view, computational linguistics can be like that—a real computational science in which the primary activities are the construction of mathematical and computational models of human language, and then undertaking efforts to solve the "equations." I have found in my work, some of which is presented here, that the formulation of a good theory for modeling language is just the first important step in a long series of sticky problems, like how to compute the model in a reasonable time.

The work herein is largely limited to the aforementioned first step, and it is
thus a contribution to that unsung subfield known as "the mathematics of language." A mathematical model is presented for certain aspects of language and its acquisition that is fitted with a computational model for solving the linguistic equations, as it were. Unfortunately, an adequate computational methodology for extracting answers in practical cases has not yet been developed, so the results here are strictly theoretical. This is not a downfall at this stage; after all, the Navier-Stokes equations were once "strictly theoretical," too.

I have undertaken to report my work and my research in this b