Short Textbooks in Logic

# Proof Theory and Algebra in Logic

Authors: Ono, Hiroakira

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• A textbook for short introductory courses on nonclassical logic at the undergraduate or graduate level

Offers a concise introduction to two major techniques in the study of nonclassical logic: proof theory and algebraic methods, and highlights a combination of proof theory with algebraic methods

Provides concrete examples showing how these techniques are applied in nonclassical logic

Demonstrates the complementary features of proof theory and algebraic methods by describing both their differences and similarities, as well as their connections

eBook 13,90 €
28,88 € (listprice)
price for Spain (gross)
valid through December 31, 2020
• ISBN 978-981-13-7997-0
• Digitally watermarked, DRM-free
• Included format: PDF, EPUB
• ebooks can be used on all reading devices
Softcover 18,71 €
36,39 € (listprice)
price for Spain (gross)
valid through December 31, 2020

This book offers a concise introduction to both proof-theory and algebraic methods, the core of the syntactic and semantic study of logic respectively. The importance of combining these two has been increasingly recognized in recent years. It highlights the contrasts between the deep, concrete results using the former and the general, abstract ones using the latter. Covering modal logics, many-valued logics, superintuitionistic and substructural logics, together with their algebraic semantics, the book also provides an introduction to nonclassical logic for undergraduate or graduate level courses.The book is divided into two parts: Proof Theory in Part I and Algebra in Logic in Part II. Part I presents sequent systems and discusses cut elimination and its applications in detail. It also provides simplified proof of cut elimination, making the topic more accessible. The last chapter of Part I is devoted to clarification of the classes of logics that are discussed in the second part.  Part II focuses on algebraic semantics for these logics. At the same time, it is a gentle introduction to the basics of algebraic logic and universal algebra with many examples of their applications in logic. Part II can be read independently of Part I, with only minimum knowledge required, and as such is suitable as a textbook for short introductory courses on algebra in logic.

Hiroakira Ono is an emeritus professor of Japan Advanced Institute for Science and Technology (JAIST). He moved to JAIST in 1993 after working at Hiroshima University for twenty years. Later he became a distinguished professor until his retirement from JAIST in 2012. His main interest is study of nonclassical logics, in particular substructural logics and intermediate logics, from both syntactic and semantical point of view. In addition to his co-authored book on substructural logics in 2007, he published six textbooks in Japanese, including those on logic and algebra, one of which gained a reputation as one of most popular textbooks on logic in Japan since its publication in 1994.

• Sequent Systems

Pages 3-22

Ono, Hiroakira

• Cut Elimination for Sequent Systems

Pages 23-33

Ono, Hiroakira

• Proof-Theoretic Analysis of Logical Properties

Pages 35-46

Ono, Hiroakira

• Modal and Substructural Logics

Pages 47-60

Ono, Hiroakira

• Deducibility and Axiomatic Extensions

Pages 61-73

Ono, Hiroakira

eBook 13,90 €
28,88 € (listprice)
price for Spain (gross)
valid through December 31, 2020
• ISBN 978-981-13-7997-0
• Digitally watermarked, DRM-free
• Included format: PDF, EPUB
• ebooks can be used on all reading devices
Softcover 18,71 €
36,39 € (listprice)
price for Spain (gross)
valid through December 31, 2020

## Bibliographic Information

Bibliographic Information
Book Title
Proof Theory and Algebra in Logic
Authors
Series Title
Short Textbooks in Logic
2019
Publisher
Springer Singapore
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-13-7997-0
DOI
10.1007/978-981-13-7997-0
Softcover ISBN
978-981-13-7996-3
Series ISSN
2522-5480
Edition Number
1
Number of Pages
VIII, 160
Number of Illustrations
4 b/w illustrations
Topics