On the Logic and Learning of Language

This book presents the author's research on automatic learning procedures for categorial grammars of natural languages. The research program spans a number of intertwined disciplines, including syntax, semantics, learnability theory, logic, and computer science. The theoretical framework employed is an extension of categorial grammar that has come to be called multimodal or type-logical grammar. The first part of the book presents an expository summary of how grammatical sentences of any language can be deduced with a specially designed logical calculus that treats syntactic categories as its formulae. Some such Universal Type Logic is posited to underlie the human language faculty, and all linguistic variation is captured by the different systems of semantic and syntactic categories which are assigned in the lexicons of different languages. The remainder of the book is devoted to the explicit formal development of computer algorithms which can learn the lexicons of type logical grammars from learning samples of annotated sentences. The annotations consist of semantic terms expressed in the lambda calculus, and may also include an unlabeled tree-structuring over the sentence. The major features of the research include the following: We show how the assumption of a universal linguistic component---the logic of language---is not incompatible with the conviction that every language needs a different system of syntactic and semantic categories for its proper description. The supposedly universal linguistic categories descending from antiquity (noun, verb, etc.) are summarily discarded. Languages are here modeled as consisting primarily of sentence trees labeled with semantic structures; a new mathematical class of such term-labeled tree languages is developed which cross-cuts the well-known Chomsky hierarchy and provides a formal restrictive condition on the nature of human languages. The human language acquisition mechanism is postulated to be biased, such that it assumes all input language samples are drawn from the above "syntactically homogeneous" class; in this way, the universal features of human languages arise not just from the innate logic of language, but also from the innate biases which govern language learning. The project on the whole represents the first complete explicit attempt to model the acquisition of human language since Steve Pinker's groundbreaking publication of "Language Learnability and Language Development" in 1984.

About the Author :
Sean Fulop received his B.Sc. in Physics from the University of Calgary in 1991 with a Linguistics minor, and abandoned Physics in favour of Linguistics. He went on to complete his Ph.D. in Linguistics at UCLA in 1999, gaining expertise in the two specialties of phonetics and mathematical linguistics. His doctoral dissertation bore the same title as the present book, and was an incomplete precursor to the research that is now being reported. In the intervening years he has held temporary lectureships and professorships, most recently appointed as Visiting Assistant Professor of Linguistics at The University of Chicago, with an affiliation to the Computer Science Department. Aside from the mathematics of language and speech, the author's greatest preoccupations are his family (including wife Jacquie and daughters Sandra and Brenna), sports cars, and progressive rock music.