Author : Frank Markham Brown
Publisher : Courier Corporation
Page : 308 pages
File Size : 29,23 MB
Release : 2012-02-10
Category : Mathematics
ISBN : 0486164594
Concise text begins with overview of elementary mathematical concepts and outlines theory of Boolean algebras; defines operators for elimination, division, and expansion; covers syllogistic reasoning, solution of Boolean equations, functional deduction. 1990 edition.
Author : Frank Markham Brown
Publisher : Courier Corporation
Page : 308 pages
File Size : 18,94 MB
Release : 2003-01-01
Category : Mathematics
ISBN : 9780486427850
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concise, newly revised edition combines the works of early logicians with recent investigations, including previously unpublished research results. Brown begins with an overview of elementary mathematical concepts and outlines the theory of Boolean algebras. Two concluding chapters deal with applications. 1990 edition.
Author : J. Eldon Whitesitt
Publisher : Courier Corporation
Page : 194 pages
File Size : 29,66 MB
Release : 2012-05-24
Category : Mathematics
ISBN : 0486158160
Introductory treatment begins with set theory and fundamentals of Boolean algebra, proceeding to concise accounts of applications to symbolic logic, switching circuits, relay circuits, binary arithmetic, and probability theory. 1961 edition.
Author : Bradford Henry Arnold
Publisher : Courier Corporation
Page : 163 pages
File Size : 18,41 MB
Release : 2011-01-01
Category : Mathematics
ISBN : 0486483851
Orignally published: Englewood Cliffs, N.J.: Prentice-Hall, 1962.
Author : Wolfgang Kunz
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 10,59 MB
Release : 2013-03-09
Category : Computers
ISBN : 1475725728
Reasoning in Boolean Networks provides a detailed treatment of recent research advances in algorithmic techniques for logic synthesis, test generation and formal verification of digital circuits. The book presents the central idea of approaching design automation problems for logic-level circuits by specific Boolean reasoning techniques. While Boolean reasoning techniques have been a central element of two-level circuit theory for many decades Reasoning in Boolean Networks describes a basic reasoning methodology for multi-level circuits. This leads to a unified view on two-level and multi-level logic synthesis. The presented reasoning techniques are applied to various CAD-problems to demonstrate their usefulness for today's industrially relevant problems. Reasoning in Boolean Networks provides lucid descriptions of basic algorithmic concepts in automatic test pattern generation, logic synthesis and verification and elaborates their intimate relationship to provide further intuition and insight into the subject. Numerous examples are provide for ease in understanding the material. Reasoning in Boolean Networks is intended for researchers in logic synthesis, VLSI testing and formal verification as well as for integrated circuit designers who want to enhance their understanding of basic CAD methodologies.
Author : Paul R. Halmos
Publisher : Courier Dover Publications
Page : 163 pages
File Size : 34,39 MB
Release : 2018-09-12
Category : Mathematics
ISBN : 0486834573
This presentation on the basics of Boolean algebra has ranked among the fundamental books on this important subject in mathematics and computing science since its initial publication in 1963. Concise and informal as well as systematic, the text draws upon lectures delivered by Professor Halmos at the University of Chicago to cover many topics in brief individual chapters. The approach is suitable for advanced undergraduates and graduate students in mathematics. Starting with Boolean rings and algebras, the treatment examines fields of sets, regular open sets, elementary relations, infinite operations, subalgebras, homomorphisms, free algebras, ideals and filters, and the homomorphism theorem. Additional topics include measure algebras, Boolean spaces, the representation theorem, duality for ideals and for homomorphisms, Boolean measure spaces, isomorphisms of factors, projective and injective algebras, and many other subjects. Several chapters conclude with stimulating exercises; the solutions are not included.
Author : George Tourlakis
Publisher : John Wiley & Sons
Page : 314 pages
File Size : 34,80 MB
Release : 2011-03-01
Category : Mathematics
ISBN : 1118030699
A comprehensive and user-friendly guide to the use of logic in mathematical reasoning Mathematical Logic presents a comprehensive introduction to formal methods of logic and their use as a reliable tool for deductive reasoning. With its user-friendly approach, this book successfully equips readers with the key concepts and methods for formulating valid mathematical arguments that can be used to uncover truths across diverse areas of study such as mathematics, computer science, and philosophy. The book develops the logical tools for writing proofs by guiding readers through both the established "Hilbert" style of proof writing, as well as the "equational" style that is emerging in computer science and engineering applications. Chapters have been organized into the two topical areas of Boolean logic and predicate logic. Techniques situated outside formal logic are applied to illustrate and demonstrate significant facts regarding the power and limitations of logic, such as: Logic can certify truths and only truths. Logic can certify all absolute truths (completeness theorems of Post and Gödel). Logic cannot certify all "conditional" truths, such as those that are specific to the Peano arithmetic. Therefore, logic has some serious limitations, as shown through Gödel's incompleteness theorem. Numerous examples and problem sets are provided throughout the text, further facilitating readers' understanding of the capabilities of logic to discover mathematical truths. In addition, an extensive appendix introduces Tarski semantics and proceeds with detailed proofs of completeness and first incompleteness theorems, while also providing a self-contained introduction to the theory of computability. With its thorough scope of coverage and accessible style, Mathematical Logic is an ideal book for courses in mathematics, computer science, and philosophy at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who wish to learn how to use logic in their everyday work.
Author : Paul Halmos
Publisher : American Mathematical Soc.
Page : 141 pages
File Size : 16,50 MB
Release : 2019-01-30
Category : Mathematics
ISBN : 1470451662
Here is an introduction to modern logic that differs from others by treating logic from an algebraic perspective. What this means is that notions and results from logic become much easier to understand when seen from a familiar standpoint of algebra. The presentation, written in the engaging and provocative style that is the hallmark of Paul Halmos, from whose course the book is taken, is aimed at a broad audience, students, teachers and amateurs in mathematics, philosophy, computer science, linguistics and engineering; they all have to get to grips with logic at some stage. All that is needed.
Author : John Gregg
Publisher : Wiley-IEEE Press
Page : 314 pages
File Size : 24,83 MB
Release : 1998-03-30
Category : Mathematics
ISBN :
Outstanding features include: a history of mathematical logic, an explanation of the logic of digital circuits, and hands-on exercises and examples.
Author : R.L. Cignoli
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 15,74 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 9401594805
This unique textbook states and proves all the major theorems of many-valued propositional logic and provides the reader with the most recent developments and trends, including applications to adaptive error-correcting binary search. The book is suitable for self-study, making the basic tools of many-valued logic accessible to students and scientists with a basic mathematical knowledge who are interested in the mathematical treatment of uncertain information. Stressing the interplay between algebra and logic, the book contains material never before published, such as a simple proof of the completeness theorem and of the equivalence between Chang's MV algebras and Abelian lattice-ordered groups with unit - a necessary prerequisite for the incorporation of a genuine addition operation into fuzzy logic. Readers interested in fuzzy control are provided with a rich deductive system in which one can define fuzzy partitions, just as Boolean partitions can be defined and computed in classical logic. Detailed bibliographic remarks at the end of each chapter and an extensive bibliography lead the reader on to further specialised topics.
