Boolean reasoning 布尔推理

A systematic treatment of Boolean reasoning, this concise, newly revised edition combines the works of early logicians with recent investigations, including previously unpublished research results. For the benefit of readers without formal training in mathematics, the text starts with an overview of elementary mathematical concepts and outlines the theory of Boolean algebras, based on Huntington's postulate. It defines operators for elimination, division, and expansion, providing a coherent and systematic basis for subsequent discussions of syllogistic reasoning, the solution of Boolean equations, and functional deduction.
　　Examples and end-of-chapter problems appear throughout the book, many taken from the design for switching systems. Two concluding chapters deal with applications; one applies Boolean reasoning to diagnostic problems, and the other discusses the design of multiple-output logic-circuits.

Dedication
Preface to the Dover Edition
1　Introduction
　1.1　Two Logical Languages
　1.2　Boolean Reasoning
　1.3　Boolean Algebra and Switching Theory
　1.4　An Approach to Boolean Problem-Solving
　1.5　Boolean Reasoning vs. Predicate Logic
　1.6　Outline
2　Fundamental Concepts
　2.1　Formulas
　2.2　Propositions and Predicates
　2.3　Sets
　2.4　Operations on Sets
　2.5　Partitions
　2.6　Relations
　2.7　Functions
　2.8　Operations and Algebraic Systems
　Exercises
3　Boolean Algebras
　3.1　Postulates for a Boolean Algebra
　3.2　Examples of Boolean Algebras
　　3.2.1　The Algebra of Classes (Subsets of a Set)
　　3.2.2　The Algebra of Propositional Functions
　　3.2.3　Arithmetic Boolean Algebras
　　3.2.4　The Two-Element Boolean Algebra.
　　3.2.5　Summary of Examples
　3.3　The Stone Representation Theorem
　3.4　The Inclusion-Relation
　　3.4.1　Intervals
　3.5　Some Useful Properties
　3.6　n-Variable Boolean Formulas
　3.7　n-Variable Boolean Functions
　3.8　Boole's Expansion Theorem
　3.9　The Minterm Canonical Form
　　3.9.1　Truth-tables
　　3.9.2　Maps
　3.10 The LSwenheim-Miiller Verification Theorem
　3.11 Switching Functions
　3.12 Incompletely-Specified Boolean Functions
　3.13 Boolean Algebras of Boolean Functions
　　3.13.1 Free Boolean Algebras
　3.14 Orthonormal Expansions
　　3.14.1 LSwenheim's Expansions
　3.15 Boolean Quotient
　3.16 The Boolean Derivative
　3.17 Recursive Definition of Boolean Functions
　3.18 What Good are "Big" Boolean Algebras?
　Exercises
4　The Blake Canonical Form
　4.1　Definitions and Terminology
　4.2　Syllogistic & Blake Canonical Formulas
　4.3　Generation of BCF(f)
　4.4　Exhaustion of Implicants
　4.5　Iterated Consensus
　　4.5.1　Quine's method
　　4.5.2　Successive extraction
　4.6　Multiplication
　　4.6.1　Recursive multiplication
　　4.6.2　Combining multiplication and iterated consensus
　　4.6.3　Unwanted syllogistic formulas
　Exercises
5 Booleam Analysis
6 Syllogistic Reasoning
7 Solution of Boolean Equations
8 Functional Deduction
9 Boolean Identification
10 Combinational Circuits:Specification&Optimization
A Syllogistic Formulas
Bibliography
Index