Mathematical Methods and Modeling for Linguistics

1. Auflage 2026
ISBN: 978-1-394-42665-2
Verlag: John Wiley & Sons Inc

Buch, Englisch, 320 Seiten

Connect mathematical concepts to linguistic theory without advanced math prerequisites

There is a strong relationship between mathematics and linguistic theory, yet students in linguistics programs rarely encounter these connections systematically. Mathematical Methods and Modeling for Linguistics demonstrates that basic theories of language can be understood mathematically and that exploring these interconnections enriches linguistic study while preparing students for advanced work in all fields of linguistics.

Assuming only minimal familiarity with mathematics, this book introduces and covers concepts such as strings and lists, sets, sentential logic, predicate logic, modal and temporal logic, type theory and lambda calculus, and formal language theory. A companion website provides sample code written in Haskell to demonstrate concepts from every chapter, though students may use any preferred programming language or ignore the code sections entirely.

Readers will also find: - A conversational writing style that removes barriers to mathematical study for students across linguistics subfields and related disciplines
- Direct applications of mathematical reasoning to phonology, morphology, and semantics, connecting abstract formalisms to concrete linguistic phenomena
- Coverage of logic traditions relevant to formal semantics, cognitive linguistics, and the philosophy of language
- Suitable as a textbook for courses in mathematical linguistics, computational linguistics, and natural language processing and for self-directed study
- Structured content supporting both classroom instruction and independent study at the advanced undergraduate and graduate levels

Designed for advanced undergraduates and graduate students in formal linguistics, computational linguistics, and natural language processing, this book also serves students of cognitive linguistics, logic, philosophy of language, and other aeras, who seek rigorous mathematical grounding in linguistic theory.

Autoren/Hrsg.

Hammond, Michael

Fachgebiete

• Geisteswissenschaften Philosophie Philosophische Logik, Argumentationstheorie
• Geisteswissenschaften Sprachwissenschaft Computerlinguistik, Korpuslinguistik
• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik

Inhaltsverzeichnis

Preface xiii
Acknowledgments xvii
About the Companion Website xix

PART I General 1

1 Prerequisites 3
1.1 What Is this Book About? 3
1.1.1 Infinite Number of Sentences 3
1.1.2 Quantifier Scope 5
1.1.3 Coordination 6
1.1.4 Phrase Structure 7
1.1.5 Phonology 8
1.1.6 Center Embedding 9
1.2 Why 10
1.2.1 Precision 11
1.2.2 Formalism 11
1.2.3 Implementation 12
1.3 Overview 12
1.4 How to Read the Book 14
1.5 How Haskell Works 14
1.6 Further Reading 16

2 Strings and Lists 19
2.1 Basic Notions in Haskell 19
2.2 Lists 23
2.3 Strings 26
2.4 Lists in Haskell 29
2.5 Definition and Proof in Haskell 35
2.6 Definition and Proof Generally 44
2.7 Summary 46
2.8 Further Reading 47
2.9 Exercises 47

3 Sets 49
3.1 Sets 49
3.2 Implementing Sets 51
3.3 Membership 58
3.4 Operations 59
3.5 Implementing Operations 60
3.6 Set-Theoretic Equalities 63
3.7 Implementing the Set-Theoretic Equalities 71
3.8 Theorems 73
3.9 Ordered Pairs, Etc 75
3.10 Implementing Ordered Pairs 76
3.11 Language Examples 79
3.11.1 Examples of Sets 79
3.11.2 Examples of Relations and Functions 79
3.12 Summary 81
3.13 Further Reading 82
3.14 Exercises 83

PART II Logics 85

4 Sentential Logic 87
4.1 The Intuition 87
4.2 Basic Syntax 87
4.2.1 Simplicity 89
4.2.2 Lack of Ambiguity 89
4.2.3 Artificiality 90
4.3 Basic Semantics 90
4.4 Rolling You Own 93
4.5 Meanings of the Connectives 100
4.5.1 Negation 101
4.5.2 Conjunction 101
4.5.3 Disjunction 102
4.5.4 Conditional102
4.5.5 Biconditional 102
4.6 How Many Connectives? 103
4.7 Implementing Sheffer Stroke 105
4.8 Native Haskell Logic 106
4.9 Tautology, Contradiction, Contingency 106
4.10 Proof 107
4.11 Implementing Proof 115
4.12 Rules of Inference 117
4.13 The Rules of Inference Implemented 120
4.14 Conditional Proof 121
4.15 Implementation 123
4.16 Indirect Proof 124
4.17 Indirect Proof Implemented 125
4.18 Language126
4.19 Summary 127
4.20 Further Reading 127
4.21 Exercises 128

5 Predicate Logic 130
5.1 Syntax 130
5.2 Semantics 132
5.3 Implementing Predicate Logic 136
5.4 A Practical Implementation 139
5.5 Laws and Rules140
5.5.1 Laws 140
5.5.2 Rules of Inference 143
5.6 Proofs 145
5.6.1 Indirect Proof 147
5.6.2 Conditional Proof 148
5.7 Proof Implementation 148
5.8 Summary 149
5.9 Further Reading 150
5.10 Exercises 150

6 Modal and Temporal Logic 152
6.1 Modal Logic152
6.1.1 Syntax of Modal Sentential Logic 152
6.1.2 Semantics of Modal Logic 153
6.1.3 Implementing Modal Logic 154
6.1.4 Different Systems of Modal Logic 159
6.1.5 Implementing Model Checks 160
6.1.6 Modal Predicate Logic 161
6.1.7 Other Interpretations of Modal Operators 162
6.2 Temporal Logic 162
6.2.1 Implementing Temporal Logic 163
6.3 Summary 166
6.4 Further Reading 166
6.5 Exercises 167

7 Type Theory and Lambda Calculus 169
7.1 Type Theory 169
7.2 Type Theory with Haskell 172
7.3 Lambda Abstraction 174
7.4 Implementing 176
7.5 Lifting 177
7.6 Sentential Logic 177
7.7 Implementing Sentential Logic 179
7.8 Math with Lambda Calculus 180
7.9 Implementing Math 181
7.10 Variables Implemented 182
7.11 Lists 187
7.12 Implementing Lists 189
7.13 Summary 190
7.14 Further Reading 190
7.15 Exercises 191

PART III Languages 193

8 Formal Language Theory 195
8.1 Languages 195
8.2 Grammars 195
8.3 Grammars with Haskell 203
8.4 Finite-State Automata 207
8.5 Implementing FSAs 214
8.6 Regular Languages 225
8.7 FSAs and Regular Languages 226
8.8 Implementing the Translation 228
8.9 Right-Linear Grammars and Automata 232
8.10 Implementing FSA Conversion 233
8.11 Closure Properties of Regular Languages 234
8.12 Implementing Intersection 235
8.13 Pumping Lemma 236
8.14 Relevance 238
8.15 Summary 240
8.16 Further Reading 241
8.17 Exercises 241

9 Formal Language Theory Continued 243
9.1 Context-Free Languages 243
9.2 Implementing CF Grammars 245
9.3 Pushdown Automata 251
9.4 Implementing PDAs 254
9.5 PDAs and CFGs 257
9.5.1 CFG to PDA 258
9.5.2 Implementing CFG to PDA 260
9.5.3 PDA to CFG262
9.6 Implementing PDA to CFG 264
9.7 Closure Properties 264
9.8 Pumping Lemma Again 265
9.9 Natural Language Syntax 267
9.10 Determinism 268
9.11 Turing Machines 269
9.12 Linear-Bounded Automata 269
9.13 Finite-State Transducers 269
9.14 Counter-Free Automata 273
9.15 Indexed Languages and Nested Stack Automata 275
9.16 Implementing Other Machines 279
9.17 Logics 284
9.17.1 Star-Free Languages 284
9.17.2 Implementing Star-Free Logic 286
9.17.3 Regular Languages 287
9.18 Summary 290
9.19 Further Reading 290
9.20 Exercises 291

Bibliography 291
Index 293

Über Autor(innen)

Michael Hammond is Professor Emeritus in the Department of Linguistics at the University of Arizona and a recognized authority in phonology, morphology, and computational linguistics. His research in phonology, morphology, and computational linguistics, with particular focus on English, Welsh, and Scottish Gaelic, has been published in numerous journal articles, chapters, and books.