- A textbook for short introductory courses on nonclassical logic at the undergraduate or graduate levelOffers 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 methodsProvides concrete examples showing how these techniques are applied in nonclassical logicDemonstrates the complementary features of proof theory and algebraic methods by describing both their differences and similarities, as well as their connections
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- About this Textbook
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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.
- About the authors
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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.
- Table of contents (10 chapters)
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Sequent Systems
Pages 3-22
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Cut Elimination for Sequent Systems
Pages 23-33
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Proof-Theoretic Analysis of Logical Properties
Pages 35-46
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Modal and Substructural Logics
Pages 47-60
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Deducibility and Axiomatic Extensions
Pages 61-73
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Table of contents (10 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Proof Theory and Algebra in Logic
- Authors
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- Hiroakira Ono
- Series Title
- Short Textbooks in Logic
- Copyright
- 2019
- Publisher
- Springer Singapore
- Copyright Holder
- 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
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