Proof theory and algebra in logic / Hiroakira Ono.
2019
QA9.54 .O46 2019eb
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Details
Title
Proof theory and algebra in logic / Hiroakira Ono.
Author
Ono, Hiroakira, author.
ISBN
9789811379970 (electronic book)
9811379971 (electronic book)
9789811379963
9811379963
9811379971 (electronic book)
9789811379963
9811379963
Published
Singapore : Springer, [2019]
Copyright
©2019
Language
English
Description
1 online resource : illustrations.
Item Number
10.1007/978-981-13-7997-0 doi
10.1007/978-981-13-7
10.1007/978-981-13-7
Call Number
QA9.54 .O46 2019eb
Dewey Decimal Classification
511.3
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed August 28, 2019).
Series
Short textbooks in logic.
Available in Other Form
Print version: 9789811379963
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Table of Contents
Introduction
Part I Proof Theory
Sequent systems
Cut elimination for sequent systems
Proof-theoretic analysis of logical properties
Modal and substructural logics
Deducibility and axiomatic extensions
Part II Algebra in Logic
Boolean algebras and classical logic
Many-valued algebras
Heyting algebras and intuitionistic logic
Logics and varieties
Residuated structures
Modal algebras
References
Index.
Part I Proof Theory
Sequent systems
Cut elimination for sequent systems
Proof-theoretic analysis of logical properties
Modal and substructural logics
Deducibility and axiomatic extensions
Part II Algebra in Logic
Boolean algebras and classical logic
Many-valued algebras
Heyting algebras and intuitionistic logic
Logics and varieties
Residuated structures
Modal algebras
References
Index.