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OverviewThe main aim of this monograph is to provide a structured study of the algebraic method in metalogic. In contrast to traditional algebraic logic, where the focus is on the algebraic forms of specific deductive systems, abstract algebraic logic is concerned with the process of algebraization itself. This book presents in a systematic way recent ideas in abstract algebraic logic centered around the notion of the Leibniz operator. The stress is put on the taxonomy of deductive systems. Isolating a list of plausible properties of the Leibniz operator serves as a basis for distinguishing certain natural classes of sentential logics. The hierarchy of deductive systems presented in the book comprises, among others, the following classes: protoalgebraic logics, equivalential logics, algebraizable logics, and Fregean logics. Because of the intimate connection between algebraic and logical structures, the book also provides a uniform treatment of various topics concerning deduction theorems and quasivarieties of algebras. The presentation of the above classes of logics is accompanied by a wealth of examples illustrating the general theory. An essential part of the book is formed by the numerous exercises integrated into the text. This book is both suitable for logically and algebraically minded graduate and advanced graduate students of mathematics, computer science and philosophy, and as a reference work for the expert. Full Product DetailsAuthor: Janusz CzelakowskiPublisher: Springer Imprint: Springer Edition: Softcover reprint of the original 1st ed. 2001 Volume: 10 Dimensions: Width: 15.50cm , Height: 2.30cm , Length: 23.50cm Weight: 0.712kg ISBN: 9789048156931ISBN 10: 9048156939 Pages: 452 Publication Date: 03 December 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of Contents0. Basic definitions and facts.- I. Protoalgebraic Logics. The Leibniz Operator.- 1. Protoalgebraic logics.- 2. Protoalgebraicity and the Deduction Theorem.- 3. Equivalential logics.- II. Algebraizable Sentential Logics.- Q. Quasivarieties of algebras.- 4. Algebraizable logics.- 5. Regularly algebraizable logics.- 6. Fregean logics.- Symbol index.- Index of definitions.Reviews'This book is an excellent and very readable introduction to the area of abstract algebraic logic. It includes recent technical results together with philosophical comments to provide a context. Many of the chapters contain exercises that give additional results and all of the chapters contain extensive end notes to guide the reader to the literature ' Mathematical Reviews, 2002f 'This book is an excellent and very readable introduction to the area of abstract algebraic logic. It includes recent technical results together with philosophical comments to provide a context. Many of the chapters contain exercises that give additional results and all of the chapters contain extensive end notes to guide the reader to the literature ' Mathematical Reviews, 2002f Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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