國立虎尾科技大學 |

Proof Theory and Algebra in Logic

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Proof Theory and Algebra in Logic/ by Hiroakira Ono.
Author:	Ono, Hiroakira.
Description:	VIII, 160 p. 4 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Logic. -
Online resource:	https://doi.org/10.1007/978-981-13-7997-0
ISBN:	9789811379970

Proof Theory and Algebra in Logic
Ono, Hiroakira.

Proof Theory and Algebra in Logic[electronic resource] /by Hiroakira Ono. - 1st ed. 2019. - VIII, 160 p. 4 illus.online resource. - 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

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

558909
Logic.

LC Class. No.: BC1-199

Dewey Class. No.: 160

Proof Theory and Algebra in Logic
LDR:03130nam a22003975i 4500 001 1003839
003 DE-He213
005 20200630140204.0
007 cr nn 008mamaa
008 210106s2019 si | s |||| 0|eng d
020 $a 9789811379970 $9 978-981-13-7997-0
024 7 $a 10.1007/978-981-13-7997-0 $2 doi
035 $a 978-981-13-7997-0
050 4 $a BC1-199
072 7 $a HPL $2 bicssc
072 7 $a PHI011000 $2 bisacsh
072 7 $a QDTL $2 thema
082 0 4 $a 160 $2 23
100 1 $a Ono, Hiroakira. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1067291
245 1 0 $a Proof Theory and Algebra in Logic $h [electronic resource] / $c by Hiroakira Ono.
250 $a 1st ed. 2019.
264 1 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2019.
300 $a VIII, 160 p. 4 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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.
650 0 $a Logic. $3 558909
650 0 $a Mathematical logic. $2 bicssc $3 810627
650 0 $a Algebra. $2 gtt $3 579870
650 0 $a Ordered algebraic structures. $3 672366
650 2 4 $a Mathematical Logic and Formal Languages. $3 670059
650 2 4 $a Mathematical Logic and Foundations. $3 669393
650 2 4 $a Order, Lattices, Ordered Algebraic Structures. $3 670104
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9789811379963
776 0 8 $i Printed edition: $z 9789811379987
830 0 $a Short Textbooks in Logic, $x 2522-5480 $3 1297196
856 4 0 $u https://doi.org/10.1007/978-981-13-7997-0
912 $a ZDB-2-REP
912 $a ZDB-2-SXPR
950 $a Religion and Philosophy (SpringerNature-41175)
950 $a Philosophy and Religion (R0) (SpringerNature-43725)