Boolean Reasoning: The Logic of Boolean Equations - Hardcover

Brown, Frank Markham

Hardcover

ISBN 10: 0792391217 ISBN 13: 9780792391210

Publisher: Springer, 1990

Synopsis

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.

About this title

About the Author

Frank Markham Brown is Professor Emeritus of the School of Engineering at the Air Force Institute of Technology.

Review

"The author writes very well . . . provid[ing] a solid foundational (graduate-level) text for mathematicians, engineers, and logicians . . . the author does a good job of drawing examples from the field of logic designed to illustrate useful applications of theory."

Edition details

• Publisher: Springer
• Publication date: 1990
• Language: English
• ISBN 10: 0792391217
• ISBN 13: 9780792391210
• Binding: Hardcover
• Number of pages: 294