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Two-Step Approaches to Natural Language Formalism [NOOK Book]

Overview

This book presents a unified formal approach to various contemporary linguistic formalisms such as Government & Binding, Minimalism or Tree Adjoining Grammar. Through a careful introduction of mathematical techniques from logic, automata theory and universal algebra, the book aims at graduate students and researchers who want to learn more about tightly constrained logical approaches to natural language syntax. Therefore it features a complete and well illustrated introduction to the connection between ...

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Two-Step Approaches to Natural Language Formalism

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Overview

This book presents a unified formal approach to various contemporary linguistic formalisms such as Government & Binding, Minimalism or Tree Adjoining Grammar. Through a careful introduction of mathematical techniques from logic, automata theory and universal algebra, the book aims at graduate students and researchers who want to learn more about tightly constrained logical approaches to natural language syntax. Therefore it features a complete and well illustrated introduction to the connection between declarative approaches formalized in monadic second-order logic (MSO) and generative ones formalized in various forms of automata as well as of tree grammars. Since MSO logic (on trees) yields only context-free languages, and at least the last two of the formalisms mentioned above clearly belong to the class of mildly context-sensitive formalisms, it becomes necessary to deal with the problem of the descriptive complexity of the formalisms involved in another way. The proposed genuinely new two-step approach overcomes this limitation of MSO logic while still retaining the desired tightly controlled formal properties.

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Product Details

Meet the Author

Frank Morawietz received his Ph. D. at the University of Tübingen, Germany.

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Table of Contents

Abstract
Acknowledgments
I Introduction 1
1 Overview 3
2 Technical preliminaries 17
II The Classical Approach
Using MSO Logic as a Description Language for Natural Language Syntax 27
3 Model-theoretic syntax and monadic second-order logic 29
4 Finite-state devices 43
5 Decidability and definability 58
6 Applications 84
7 Intermediate conclusion 106
III Two Steps Are Better Than One
Extending the Use of MSO Logic to Non-Context-Free Linguistic Formalisms 109
8 Overview of the two-step approach 111
9 Non-context-freeness of natural language 115
10 The first step: Lifting 131
11 The second step: Reconstruction 155
IV Conclusion and Outlook 183
12 Conclusion 185
13 Outlook 187
V Appendix 191
A: Acronyms 193
B MONA code 194
C Additional MSO Definitions 207
D Prolog Code 209
Endnotes 218
Bibliography 223
Mathematical Symbols 240
Index 243
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