Proof Theory and Algebra in Logic

Beschreibung

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 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.
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 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.
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

Autor*in

Hiroakira Ono

Themen in »Proof Theory and Algebra in Logic«

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

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“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)

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