Overview
- 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
Part of the book series: Short Textbooks in Logic (STXLO)
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Table of contents (10 chapters)
-
Algebra in Logic
Keywords
- Proof theory introduction
- Algebraic semantics
- Nonclassical logics
- Sequent systems
- Cut elimination
- Algebraic logic
- Universal algebra
- Deduction theorems
- Boolean algebras
- Algebra Logic
- syntactic and semantic logic
- Algebraic method logic
- Algebraic method syntactic logic
- Algebraic method semantic logic
- Modal Logic Introduction
- many-valued logic introduction
- superintuitionistic logic introduction
- substructural logic introduction
- algebraic semantics introduction
- nonclassical logic introduction
About this book
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 inthe 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.
Reviews
“I cannot think of a better textbook as the backbone of an introductory course in proof theory, given how clear and self-contained the material is. … ‘Proof Theory and Algebra in Logic’ is an inspiring book that sows the seeds for further studies, and it is the perfect bridge towards more advanced research topics.” (Gianluca Caterina, MAA Reviews, June 21, 2021)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Proof Theory and Algebra in Logic
Authors: Hiroakira Ono
Series Title: Short Textbooks in Logic
DOI: https://doi.org/10.1007/978-981-13-7997-0
Publisher: Springer Singapore
eBook Packages: Religion and Philosophy, Philosophy and Religion (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2019
Softcover ISBN: 978-981-13-7996-3Published: 19 August 2019
eBook ISBN: 978-981-13-7997-0Published: 02 August 2019
Series ISSN: 2522-5480
Series E-ISSN: 2522-5499
Edition Number: 1
Number of Pages: VIII, 160
Number of Illustrations: 4 b/w illustrations
Topics: Logic, Mathematical Logic and Formal Languages, Mathematical Logic and Foundations, Order, Lattices, Ordered Algebraic Structures