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Proof Theory and Algebra in Logic

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Proof Theory and Algebra in Logic/ by Hiroakira Ono.
作者:	Ono, Hiroakira.
面頁冊數:	VIII, 160 p. 4 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Logic. -
電子資源:	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

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