Protoalgebraic Logics

1. Front Matter

   Pages i-xi

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2. Introduction

   1. Introduction

      • Janusz Czelakowski

      Pages 1-20

3. Basic Definitions and Facts

   1. Basic Definitions and Facts

      • Janusz Czelakowski

      Pages 21-66

4. Protoalgebraic Logics. The Leibniz Operator

   1. Front Matter

      Pages 67-67

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   2. Protoalgebraic Logics

      • Janusz Czelakowski

      Pages 69-122

   3. Protoalgebraicity and the Deduction Theorem

      • Janusz Czelakowski

      Pages 123-184

   4. Equivalential Logics

      • Janusz Czelakowski

      Pages 185-242

5. Algebraizable Sentential Logics

   1. Front Matter

      Pages 243-243

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   2. Quasivarieties of Algebras

      • Janusz Czelakowski

      Pages 245-285

   3. Algebraizable Logics

      • Janusz Czelakowski

      Pages 287-345

   4. Regularly Algebraizable Logics

      • Janusz Czelakowski

      Pages 347-371

   5. Fregean Logics

      • Janusz Czelakowski

      Pages 373-418

6. Back Matter

   Pages 419-452

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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

`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

• Institute of Mathematics, Opole University, Opole, Poland

  Janusz Czelakowski

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