Boolean Reasoning de Frank Markham Brown

Boolean Reasoning

Frank Markham Brown

en Limba Engleză Paperback – 16 mar 2012

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concise, newly revised edition combines the works of early logicians with recent investigations, including previously unpublished research results.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.

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Preț

Express

Paperback (2)

90^.91 lei 3-5 săpt.

Dover Publications – 16 mar 2012

90^.91 lei 3-5 săpt.

Springer Us – 14 noi 2012

907^.85 lei 6-8 săpt.

Hardback (1)

913^.62 lei 6-8 săpt.

Springer Us – aug 1990

913^.62 lei 6-8 săpt.

Cuprins

1 Fundamental Concepts.- 1.1 Formulas.- 1.2 Propositions and Predicates.- 1.3 Sets.- 1.4 Operations on Sets.- 1.5 Partitions.- 1.6 Relations.- 1.7 Functions.- 1.8 Operations and Algebraic Systems.- 2 Boolean Algebras.- 2.1 Postulates for a Boolean Algebra.- 2.2 Examples of Boolean Algebras.- 2.3 The Stone Representation Theorem.- 2.4 The Inclusion-Relation.- 2.5 Some Useful Properties.- 2.6 n-Variable Boolean Formulas.- 2.7 n-Variable Boolean Functions.- 2.8 Boole’s Expansion Theorem.- 2.9 The Minterm Canonical Form.- 2.10 The Löwenheim-Müller Verification Theorem.- 2.11 Switching Functions.- 2.12 Incompletely-Specified Boolean Functions.- 2.13 Boolean Algebras of Boolean Functions.- 2.14 Orthonormal Expansions.- 2.15 Boolean Quotient.- 2.16 The Boolean Derivative.- 2.17 Recursive Definition of Boolean Functions.- 2.18 What Good are “Big” Boolean Algebras?.- 3 The Blake Canonical Form.- 3.1 Definitions and Terminology.- 3.2 Syllogistic & Blake Canonical Formulas.- 3.3 Generation of BCF(f).- 3.4 Exhaustion of Implicants.- 3.5 Iterated Consensus.- 3.6 Multiplication.- 4 Boolean Analysis.- 4.1 Review of Elementary Properties.- 4.2 Boolean Systems.- 4.3 Reduction.- 4.4 The Extended Verification Theorem.- 4.5 Poretsky’s Law of Forms.- 4.6 Boolean Constraints.- 4.7 Elimination.- 4.8 Eliminants.- 4.9 Rudundant Variables.- 4.10 Substitution.- 4.11 The Tautology Problem.- 5 Syllogistic Reasoning.- 5.1 The Principle of Assertion.- 5.2 Deduction by Consensus.- 5.3 Syllogistic Formulas.- 5.4 Clausal Form.- 5.5 Producing and Verifying Consequents.- 5.6 Class-Logic.- 5.7 Selective Deduction.- 5.8 Functional Relations.- 5.9 Dependent Sets of Functions.- 5.10 Sum-to-One Subsets.- 5.11 Irredundant Formulas.- 6 Solution of Boolean Equations.- 6.1 Particular Solutions andConsistency.- 6.2 General Solutions.- 6.3 Subsumptive General Solutions.- 6.4 Parametric General Solutions.- 7 Functional Deduction.- 7.1 Functionally Deducible Arguments.- 7.2 Eliminable and Determining Subsets.- 8 Boolean Identification.- 8.1 Parametric and Diagnostic Models.- 8.2 Adaptive Identification.- 9 Recursive Realizations of Combinational Circuits.- 9.1 The Design-Process.- 9.2 Specifications.- 9.3 Tabular Specifications.- 9.4 Strongly Combinational Solutions.- 9.5 Least-Cost Recursive Solutions.- 9.6 Constructing Recursive Solutions.- A Syllogistic Formulas.- A.1 Absorptive Formulas.- A.2 Syllogistic Formulas.- A.3 Prime Implicants.- A.4 The Blake Canonical Form.