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Proof theory and algebra in logic

Ono, Hiroakira.

Proof theory and algebra in logic

Record Type:	Electronic resources : Monograph/item
Title/Author:	Proof theory and algebra in logicby Hiroakira Ono.
Author:	Ono, Hiroakira.
Published:	Singapore :Springer Singapore :2019.
Description:	viii, 160 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Proof theory.
Online resource:	https://doi.org/10.1007/978-981-13-7997-0
ISBN:	9789811379970$q(electronic bk.)

Proof theory and algebra in logic
Ono, Hiroakira.

Proof theory and algebra in logic[electronic resource] /by Hiroakira Ono. - Singapore :Springer Singapore :2019. - viii, 160 p. :ill., digital ;24 cm. - Short textbooks in logic,2522-5480. - Short textbooks in logic..

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.

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.

ISBN: 9789811379970$q(electronic bk.)

Standard No.: 10.1007/978-981-13-7997-0doiSubjects--Topical Terms:

190840
Proof theory.

LC Class. No.: QA9.54 / .O564 2019

Dewey Class. No.: 511.3

Proof theory and algebra in logic
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245 1 0 $a Proof theory and algebra in logic $h [electronic resource] / $c by Hiroakira Ono.
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300 $a viii, 160 p. : $b ill., digital ; $c 24 cm.
490 1 $a Short textbooks in logic, $x 2522-5480
505 0 $a 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.
520 $a 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.
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650 2 4 $a Mathematical Logic and Foundations. $3 274479
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