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Universal Algebra, Algebraic Logic, and Databases

  • Book
  • © 1994

Overview

Authors:
  1. B. Plotkin

    1. Hebrew University, Jerusalem, Israel

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Part of the book series: Mathematics and Its Applications (MAIA, volume 272)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xv
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  2. Introduction

    1. Front Matter

      Pages 1-1
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    2. General View on Objectives and Contents of the Book

      • B. Plotkin
      Pages 3-25

  3. Universal Algebra

    1. Front Matter

      Pages 27-27
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    2. Sets, Algebras, Models

      • B. Plotkin
      Pages 29-46

    3. Fundamental Structures

      • B. Plotkin
      Pages 47-63

    4. Categories

      • B. Plotkin
      Pages 65-84

    5. The Category of Sets. Topoi. Fuzzy Sets

      • B. Plotkin
      Pages 85-114

    6. Varieties of Algebras. Axiomatizable Classes

      • B. Plotkin
      Pages 115-128

    7. Category Algebra and Algebraic Theories

      • B. Plotkin
      Pages 129-152

  4. Algebraic Logic

    1. Front Matter

      Pages 153-153
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    2. Boolean Algebras and Propositional Calculus

      • B. Plotkin
      Pages 155-171

    3. Halmos Algebras and Predicate Calculus

      • B. Plotkin
      Pages 173-200

    4. Specialized Halmos Algebras

      • B. Plotkin
      Pages 201-228

    5. Connections With Model Theory

      • B. Plotkin
      Pages 229-246

    6. The Categorial Approach to Algebraic Logic

      • B. Plotkin
      Pages 247-274

  5. Databases — Algebraic Aspects

    1. Front Matter

      Pages 275-275
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    2. Algebraic Model of a Database

      • B. Plotkin
      Pages 277-304

    3. Equivalence and Reorganization of Databases

      • B. Plotkin
      Pages 305-328

    4. Symmetries of Relations and Galois Theory of Databases

      • B. Plotkin
      Pages 329-363
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Keywords

About this book

Modern algebra, which not long ago seemed to be a science divorced from real life, now has numerous applications. Many fine algebraic structures are endowed with meaningful contents. Now and then practice suggests new and unexpected structures enriching algebra. This does not mean that algebra has become merely a tool for applications. Quite the contrary, it significantly benefits from the new connections. The present book is devoted to some algebraic aspects of the theory of databases. It consists of three parts. The first part contains information about universal algebra, algebraic logic is the subject of the second part, and the third one deals with databases. The algebraic material of the flI'St two parts serves the common purpose of applying algebra to databases. The book is intended for use by mathematicians, and mainly by algebraists, who realize the necessity to unite theory and practice. It is also addressed to programmers, engineers and all potential users of mathematics who want to construct their models with the help of algebra and logic. Nowadays, the majority of professional mathematicians work in close cooperation with representatives of applied sciences and even industrial technology. It is neces­ sary to develop an ability to see mathematics in different particular situations. One of the tasks of this book is to promote the acquisition of such skills.

Authors and Affiliations

  • Hebrew University, Jerusalem, Israel

    B. Plotkin

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