© 2001

Protoalgebraic Logics


Part of the Trends in Logic book series (TREN, volume 10)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Introduction

    1. Janusz Czelakowski
      Pages 1-20
  3. Basic Definitions and Facts

    1. Janusz Czelakowski
      Pages 21-66
  4. Protoalgebraic Logics. The Leibniz Operator

    1. Front Matter
      Pages 67-67
    2. Janusz Czelakowski
      Pages 69-122
    3. Janusz Czelakowski
      Pages 123-184
    4. Janusz Czelakowski
      Pages 185-242
  5. Algebraizable Sentential Logics

    1. Front Matter
      Pages 243-243
    2. Janusz Czelakowski
      Pages 245-285
    3. Janusz Czelakowski
      Pages 287-345
    4. Janusz Czelakowski
      Pages 347-371
    5. Janusz Czelakowski
      Pages 373-418
  6. Back Matter
    Pages 419-452

About this book


The main aim of this book is to present recent ideas in logic centered around the notion of a consequence operation. We wish to show these ideas in a factually and materially connected way, i.e., in the form of a consistent theory derived from several simple assumptions and definitions. These ideas have arisen in many research centers. The thorough study of their history can certainly be an exciting task for the historian of logic; in the book this aspect of the theory is being played down. The book belongs to abstract algebraic logic, the area of research that explores to a large extent interconnections between algebra and logic. The results presented here concern logics defined in zero-order languages (Le., quantifier-free sentential languages without predicate symbols). The reach of the theory expounded in the book is, in fact, much wider. The theory is also valid for logics defined in languages of higer orders. The problem of transferring the theory to the level of first-order languages has been satisfactorily solved and new ideas within this area have been put forward in the work of Blok and Pigozzi [1989].


algebra computer science logic mathematics

Authors and affiliations

  1. 1.Institute of MathematicsOpole UniversityOpolePoland

Bibliographic information

  • Book Title Protoalgebraic Logics
  • Authors Janusz Czelakowski
  • Series Title Trends in Logic
  • DOI
  • Copyright Information Springer Science+Business Media B.V. 2001
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-7923-6940-0
  • Softcover ISBN 978-90-481-5693-1
  • eBook ISBN 978-94-017-2807-2
  • Series ISSN 1572-6126
  • Series E-ISSN 2212-7313
  • Edition Number 1
  • Number of Pages XII, 452
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Mathematical Logic and Foundations
  • Buy this book on publisher's site
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`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