A Formal Introduction

By Alan Bale and Charles Reiss

An introduction to generative phonology using tools of basic set theory, logic, and combinatorics.
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An introduction to generative phonology using tools of basic set theory, logic, and combinatorics.

This textbook introduces phonological theory as a branch of cognitive science for students with minimal background in linguistics. The authors use basic math and logic, including set theory, some rules of inference, and basic combinatorics, to explain phonology, and use phonology to teach the math and logic. The text is unique in its focus on logical analysis, its use of toy data, and its provision of some interpretation rules for its phonological rule syntax.

The book's eight parts cover preliminary and background material; the motivation for phonological rules; the development of a formal model for phonological rules; the basic logic of neutralization rules; the traditional notions of allophony and complementary distribution; the logic of rule interaction, presented in terms of function composition; a survey of such issues as length, tone, syllabification, and metathesis; and features and feature logic, with a justification of decomposing segments into features and treating segments as sets of (valued) features. End-of-chapter exercises help students apply the concepts presented. Much of the discussion and many of the exercises rely on toy data, but more “real” data is included toward the end of the book. Exercises available online can be used as homework or in-class quizzes.


$45.00 X ISBN: 9780262038386 608 pp. | 7 in x 9 in 6 b&w illus.


  • This unique and innovative textbook elevates phonological analysis by teaching it hand in hand with mathematical and logical reasoning. Every student of linguistics should read this book.

    Jeffrey Heinz

    Professor, Department of Linguistics, Institute of Advanced Computational Science, Stony Brook University; coauthor of Grammatical Inference for Computational Linguistics: Synthesis Lectures on Human Language Technologies

  • This book, taking nothing for granted, meticulously captures the beauty of phonology as a formal system within the human mind. With vivid and memorable explanations, it opens new possibilities for the fully integrated teaching of phonology with mathematics, philosophy, and computer science.

    Yuni Kim

    Lecturer in Phonology, University of Essex

  • This is a unique and very successful textbook. It is formally rigorous, addressing many issues of how phonological analyses actually work that are left out of other books. But it is also very didactic in introducing all of the concepts in manageable servings and offers a generous number of practice problems tailored directly to the issues at hand.

    William J. Idsardi

    Professor, Department of Linguistics and Program in Neuroscience and Cognitive Science, University of Maryland

  • Phonology was arguably the first among the cognitive sciences to receive rigorous mathematical formalization, but this is sometimes forgotten. In the first book to lay out the field's very precise logical modes of argumentation explicitly for the beginning student, Bale and Reiss show how much can be gained from a cognitive approach to phonology by means of formal tools.

    Marc van Oostendorp

    Meertens Instituut, Royal Netherlands Academy of Arts and Sciences