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Boolean Reasoning - The Logic of Boolean Equations (Paperback, Softcover reprint of the original 1st ed. 1990)
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Boolean Reasoning - The Logic of Boolean Equations (Paperback, Softcover reprint of the original 1st ed. 1990)
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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.
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