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© 1990

Boolean Reasoning

The Logic of Boolean Equations

Book

Table of contents

  1. Front Matter
    Pages i-xix
  2. Frank Markham Brown
    Pages 1-21
  3. Frank Markham Brown
    Pages 23-69
  4. Frank Markham Brown
    Pages 71-86
  5. Frank Markham Brown
    Pages 87-122
  6. Frank Markham Brown
    Pages 123-152
  7. Frank Markham Brown
    Pages 153-179
  8. Frank Markham Brown
    Pages 181-192
  9. Frank Markham Brown
    Pages 193-210
  10. Frank Markham Brown
    Pages 211-237
  11. Back Matter
    Pages 239-273

About this book

Introduction

This book is about the logic of Boolean equations. Such equations were central in the "algebra of logic" created in 1847 by Boole [12, 13] and devel­ oped by others, notably Schroder [178], in the remainder of the nineteenth century. Boolean equations are also the language by which digital circuits are described today. Logicians in the twentieth century have abandoned Boole's equation­ based logic in favor of the more powerful predicate calculus. As a result, digital engineers-and others who use Boole's language routinely-remain largely unaware of its utility as a medium for reasoning. The aim of this book, accordingly, is to is to present a systematic outline of the logic of Boolean equations, in the hope that Boole's methods may prove useful in solving present-day problems. Two Logical Languages Logic seeks to reduce reasoning to calculation. Two main languages have been developed to achieve that object: Boole's "algebra of logic" and the predicate calculus. Boole's approach was to represent classes (e. g. , happy creatures, things productive of pleasure) by symbols and to represent logical statements as equations to be solved. His formulation proved inadequate, however, to represent ordinary discourse. A number of nineteenth-century logicians, including Jevons [94], Poretsky [159], Schroder [178], Venn [210], and Whitehead [212, 213], sought an improved formulation based on ex­ tensions or modifications of Boole's algebra. These efforts met with only limited success.

Keywords

Algebra of Logic circuit design logic model svcrsp13 testing

Authors and affiliations

  1. 1.Air Force Institute of TechnologyUSA

Bibliographic information

  • Book Title Boolean Reasoning
  • Book Subtitle The Logic of Boolean Equations
  • Authors Frank Markham Brown
  • DOI https://doi.org/10.1007/978-1-4757-2078-5
  • Copyright Information Springer-Verlag US 1990
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-7923-9121-0
  • Softcover ISBN 978-1-4757-2080-8
  • eBook ISBN 978-1-4757-2078-5
  • Edition Number 1
  • Number of Pages XVIII, 276
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Circuits and Systems
    Electrical Engineering
  • Buy this book on publisher's site