Logical Arithmetic

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Arithmetic And Logic In Computer Systems

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Author : Mi Lu
language : en
Publisher: John Wiley & Sons
Release Date : 2005-03-04

Arithmetic And Logic In Computer Systems written by Mi Lu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-04 with Computers categories.

Arithmetic and Logic in Computer Systems provides a useful guide to a fundamental subject of computer science and engineering. Algorithms for performing operations like addition, subtraction, multiplication, and division in digital computer systems are presented, with the goal of explaining the concepts behind the algorithms, rather than addressing any direct applications. Alternative methods are examined, and explanations are supplied of the fundamental materials and reasoning behind theories and examples. No other current books deal with this subject, and the author is a leading authority in the field of computer arithmetic. The text introduces the Conventional Radix Number System and the Signed-Digit Number System, as well as Residue Number System and Logarithmic Number System. This book serves as an essential, up-to-date guide for students of electrical engineering and computer and mathematical sciences, as well as practicing engineers and computer scientists involved in the design, application, and development of computer arithmetic units.

A Friendly Introduction To Mathematical Logic

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Author : Christopher C. Leary
language : en
Publisher: Lulu.com
Release Date : 2015

A Friendly Introduction To Mathematical Logic written by Christopher C. Leary and has been published by Lulu.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Education categories.

At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.

The Foundations Of Arithmetic

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Author : Gottlob Frege
language : en
Publisher: Addison-Wesley Longman
Release Date : 2007

The Foundations Of Arithmetic written by Gottlob Frege and has been published by Addison-Wesley Longman this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

Part of the Longman Library of Primary Sources in Philosophy," this edition ofFrege's" Foundations of Arithmetic" is framed by a pedagogical structure designed to make this important work of philosophy more accessible and meaningful for readers. A General Introduction includes the work's historical context, a discussion of historical influences, and biographical information on Gottlob Frege. The conclusion discusses how the work has influenced other philosophers and why it is important today. Annotations and notes from the editor clarify difficult passages for greater understanding, and a bibliography gives the reader additional resources for further study.

Mathematical Logic

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Author : George Tourlakis
language : en
Publisher: John Wiley & Sons
Release Date : 2011-03-01

Mathematical Logic written by George Tourlakis and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-01 with Mathematics categories.

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.

Logic Of Arithmetic

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Author : Walter Felscher
language : en
Publisher: CRC Press
Release Date : 2000-05-30

Logic Of Arithmetic written by Walter Felscher and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-30 with Mathematics categories.

For propositional logic it can be decided whether a formula has a deduction from a finite set of other formulas. This volume begins with a method to decide this for the quantified formulas of those fragments of arithmetic which express the properties of order-plus-successor and of order-plus-addition (Pressburger arithmetic). It makes use of an algorithm eliminating quantifiers which, in turn, is also applied to obtain consistency proofs for these fragments.

Towards An Arithmetical Logic

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Author : Yvon Gauthier
language : en
Publisher: Birkhäuser
Release Date : 2015-09-24

Towards An Arithmetical Logic written by Yvon Gauthier and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-24 with Mathematics categories.

This book offers an original contribution to the foundations of logic and mathematics and focuses on the internal logic of mathematical theories, from arithmetic or number theory to algebraic geometry. Arithmetical logic is the term used to refer to the internal logic of classical arithmetic, here called Fermat-Kronecker arithmetic and combines Fermat’s method of infinite descent with Kronecker’s general arithmetic of homogeneous polynomials. The book also includes a treatment of theories in physics and mathematical physics to underscore the role of arithmetic from a constructivist viewpoint. The scope of the work intertwines historical, mathematical, logical and philosophical dimensions in a unified critical perspective; as such, it will appeal to a broad readership from mathematicians to logicians, to philosophers interested in foundational questions. Researchers and graduate students in the fields of philosophy and mathematics will benefit from the author’s critical approach to the foundations of logic and mathematics.

Arithmetic It S Logical And Historical Development

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Author : Benjamin Gratz Brown
language : en
Publisher:
Release Date : 1877

Arithmetic It S Logical And Historical Development written by Benjamin Gratz Brown and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1877 with Arithmetic categories.

Bounded Arithmetic Propositional Logic And Complexity Theory

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Author : Jan Krajicek
language : en
Publisher: Cambridge University Press
Release Date : 1995-11-24

Bounded Arithmetic Propositional Logic And Complexity Theory written by Jan Krajicek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-24 with Computers categories.

Discusses the deep connections between logic and complexity theory, and lists a number of intriguing open problems.

Lectures On The Logic Of Arithmetic

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Author : Mary Everest Boole
language : en
Publisher:
Release Date : 1903

Lectures On The Logic Of Arithmetic written by Mary Everest Boole and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1903 with Arithmetic categories.

Gottlob Frege Basic Laws Of Arithmetic

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Author : Gottlob Frege
language : en
Publisher:
Release Date : 2013-10

Gottlob Frege Basic Laws Of Arithmetic written by Gottlob Frege and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10 with Mathematics categories.

This is the first complete English translation of Gottlob Frege's Grundgesetze der Arithmetik (1893 and 1903), with introduction and annotation. As the culmination of his ground-breaking work in the philosophy of logic and mathematics, Frege here tried to show how the fundamental laws of arithmetic could be derived from purely logical principles.