Alan Turings Systems Of Logic

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Alan Turing's Systems of Logic

Author : Andrew W. Appel
Publisher : Princeton University Press
ISBN 13 : 0691164738
Total Pages : 160 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Alan Turing's Systems of Logic by : Andrew W. Appel

Download or read book Alan Turing's Systems of Logic written by Andrew W. Appel and published by Princeton University Press. This book was released on 2014-11-16 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: A facsimile edition of Alan Turing's influential Princeton thesis Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912–1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world—including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene—were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton. A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal—a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine. Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science.

Alan Turing's Systems of Logic

Author : Andrew W. Appel
Publisher : Princeton University Press
ISBN 13 : 1400843219
Total Pages : 164 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Alan Turing's Systems of Logic by : Andrew W. Appel

Download or read book Alan Turing's Systems of Logic written by Andrew W. Appel and published by Princeton University Press. This book was released on 2021-10-12 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: A facsimile edition of Alan Turing's influential Princeton thesis Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912–1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world—including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene—were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton. A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal—a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine. Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science.

The Essential Turing

Author : B. J. Copeland
Publisher : Clarendon Press
ISBN 13 : 0191606863
Total Pages : 1428 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis The Essential Turing by : B. J. Copeland

Download or read book The Essential Turing written by B. J. Copeland and published by Clarendon Press. This book was released on 2004-09-09 with total page 1428 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ideas that gave birth to the computer age Alan Turing, pioneer of computing and WWII codebreaker, was one of the most important and influential thinkers of the twentieth century. In this volume for the first time his key writings are made available to a broad, non-specialist readership. They make fascinating reading both in their own right and for their historic significance: contemporary computational theory, cognitive science, artificial intelligence, and artificial life all spring from this ground-breaking work, which is also rich in philosophical and logical insight.

Computability

Author : B. Jack Copeland
Publisher : MIT Press
ISBN 13 : 0262018993
Total Pages : 373 pages
Book Rating : 4.2/5 (62 download)

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Book Synopsis Computability by : B. Jack Copeland

Download or read book Computability written by B. Jack Copeland and published by MIT Press. This book was released on 2013-06-07 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computer scientists, mathematicians, and philosophers discuss the conceptual foundations of the notion of computability as well as recent theoretical developments. In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo Church, and others established the theoretical basis for computability. This work, advancing precise characterizations of effective, algorithmic computability, was the culmination of intensive investigations into the foundations of mathematics. In the decades since, the theory of computability has moved to the center of discussions in philosophy, computer science, and cognitive science. In this volume, distinguished computer scientists, mathematicians, logicians, and philosophers consider the conceptual foundations of computability in light of our modern understanding.Some chapters focus on the pioneering work by Turing, Gödel, and Church, including the Church-Turing thesis and Gödel's response to Church's and Turing's proposals. Other chapters cover more recent technical developments, including computability over the reals, Gödel's influence on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our theoretical understanding of online and interactive computing; and others relate computability and complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of mathematics.ContributorsScott Aaronson, Dorit Aharonov, B. Jack Copeland, Martin Davis, Solomon Feferman, Saul Kripke, Carl J. Posy, Hilary Putnam, Oron Shagrir, Stewart Shapiro, Wilfried Sieg, Robert I. Soare, Umesh V. Vazirani

Alan Turing

Author : S. Barry Cooper
Publisher : Elsevier
ISBN 13 : 0123870127
Total Pages : 937 pages
Book Rating : 4.1/5 (238 download)

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Book Synopsis Alan Turing by : S. Barry Cooper

Download or read book Alan Turing written by S. Barry Cooper and published by Elsevier. This book was released on 2013-03-18 with total page 937 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP, readers will find many of the most significant contributions from the four-volume set of the Collected Works of A. M. Turing. These contributions, together with commentaries from current experts in a wide spectrum of fields and backgrounds, provide insight on the significance and contemporary impact of Alan Turing's work. Offering a more modern perspective than anything currently available, Alan Turing: His Work and Impact gives wide coverage of the many ways in which Turing's scientific endeavors have impacted current research and understanding of the world. His pivotal writings on subjects including computing, artificial intelligence, cryptography, morphogenesis, and more display continued relevance and insight into today's scientific and technological landscape. This collection provides a great service to researchers, but is also an approachable entry point for readers with limited training in the science, but an urge to learn more about the details of Turing's work. - 2013 winner of the prestigious R.R. Hawkins Award from the Association of American Publishers, as well as the 2013 PROSE Awards for Mathematics and Best in Physical Sciences & Mathematics, also from the AAP - Named a 2013 Notable Computer Book in Computing Milieux by Computing Reviews - Affordable, key collection of the most significant papers by A.M. Turing - Commentary explaining the significance of each seminal paper by preeminent leaders in the field - Additional resources available online

Alan Turing: Life and Legacy of a Great Thinker

Author : Christof Teuscher
Publisher : Springer Science & Business Media
ISBN 13 : 3662056429
Total Pages : 553 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Alan Turing: Life and Legacy of a Great Thinker by : Christof Teuscher

Download or read book Alan Turing: Life and Legacy of a Great Thinker written by Christof Teuscher and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a distinguished cast of contributors, Alan Turing: Life and Legacy of a Great Thinker is the definitive collection of essays in commemoration of the 90th birthday of Alan Turing. This fascinating text covers the rich facets of his life, thoughts, and legacy, but also sheds some light on the future of computing science with a chapter contributed by visionary Ray Kurzweil, winner of the 1999 National Medal of Technology. Further, important contributions come from the philosopher Daniel Dennett, the Turing biographer Andrew Hodges, and from the distinguished logician Martin Davis, who provides a first critical essay on an emerging and controversial field termed "hypercomputation".

Principia Mathematica

Author : Alfred North Whitehead
Publisher :
ISBN 13 :
Total Pages : 688 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Principia Mathematica by : Alfred North Whitehead

Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Annotated Turing

Author : Charles Petzold
Publisher : John Wiley & Sons
ISBN 13 : 0470229055
Total Pages : 391 pages
Book Rating : 4.4/5 (72 download)

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Book Synopsis The Annotated Turing by : Charles Petzold

Download or read book The Annotated Turing written by Charles Petzold and published by John Wiley & Sons. This book was released on 2008-06-16 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Programming Legend Charles Petzold unlocks the secrets of the extraordinary and prescient 1936 paper by Alan M. Turing Mathematician Alan Turing invented an imaginary computer known as the Turing Machine; in an age before computers, he explored the concept of what it meant to be computable, creating the field of computability theory in the process, a foundation of present-day computer programming. The book expands Turing’s original 36-page paper with additional background chapters and extensive annotations; the author elaborates on and clarifies many of Turing’s statements, making the original difficult-to-read document accessible to present day programmers, computer science majors, math geeks, and others. Interwoven into the narrative are the highlights of Turing’s own life: his years at Cambridge and Princeton, his secret work in cryptanalysis during World War II, his involvement in seminal computer projects, his speculations about artificial intelligence, his arrest and prosecution for the crime of "gross indecency," and his early death by apparent suicide at the age of 41.

New Computational Paradigms

Author : S.B. Cooper
Publisher : Springer Science & Business Media
ISBN 13 : 0387685464
Total Pages : 560 pages
Book Rating : 4.3/5 (876 download)

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Book Synopsis New Computational Paradigms by : S.B. Cooper

Download or read book New Computational Paradigms written by S.B. Cooper and published by Springer Science & Business Media. This book was released on 2007-11-28 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.

Three Views of Logic

Author : Donald W. Loveland
Publisher : Princeton University Press
ISBN 13 : 140084875X
Total Pages : 339 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Three Views of Logic by : Donald W. Loveland

Download or read book Three Views of Logic written by Donald W. Loveland and published by Princeton University Press. This book was released on 2014-01-26 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first interdisciplinary textbook to introduce students to three critical areas in applied logic Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic Treats traditional logic in a modern format Presents relevance logic with applications Provides an ideal text for a variety of one-semester upper-level undergraduate courses

Mathematical Logic

Author : R.O. Gandy
Publisher : Elsevier
ISBN 13 : 0080535925
Total Pages : 307 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Mathematical Logic by : R.O. Gandy

Download or read book Mathematical Logic written by R.O. Gandy and published by Elsevier. This book was released on 2001-12-05 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Logic is a collection of the works of one of the leading figures in 20th-century science. This collection of A.M. Turing's works is intended to include all his mature scientific writing, including a substantial quantity of unpublished material. His work in pure mathematics and mathematical logic extended considerably further; the work of his last years, on morphogenesis in plants, is also of the greatest originality and of permanent importance. This book is divided into three parts. The first part focuses on computability and ordinal logics and covers Turing's work between 1937 and 1938. The second part covers type theory; it provides a general introduction to Turing's work on type theory and covers his published and unpublished works between 1941 and 1948. Finally, the third part focuses on enigmas, mysteries, and loose ends. This concluding section of the book discusses Turing's Treatise on the Enigma, with excerpts from the Enigma Paper. It also delves into Turing's papers on programming and on minimum cost sequential analysis, featuring an excerpt from the unpublished manuscript. This book will be of interest to mathematicians, logicians, and computer scientists.

The Universal Computer

Author : Martin Davis
Publisher : CRC Press
ISBN 13 : 1466505206
Total Pages : 232 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis The Universal Computer by : Martin Davis

Download or read book The Universal Computer written by Martin Davis and published by CRC Press. This book was released on 2018-10-08 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: The breathtakingly rapid pace of change in computing makes it easy to overlook the pioneers who began it all. Written by Martin Davis, respected logician and researcher in the theory of computation, The Universal Computer: The Road from Leibniz to Turing explores the fascinating lives, ideas, and discoveries of seven remarkable mathematicians. It tells the stories of the unsung heroes of the computer age – the logicians. The story begins with Leibniz in the 17th century and then focuses on Boole, Frege, Cantor, Hilbert, and Gödel, before turning to Turing. Turing’s analysis of algorithmic processes led to a single, all-purpose machine that could be programmed to carry out such processes—the computer. Davis describes how this incredible group, with lives as extraordinary as their accomplishments, grappled with logical reasoning and its mechanization. By investigating their achievements and failures, he shows how these pioneers paved the way for modern computing. Bringing the material up to date, in this revised edition Davis discusses the success of the IBM Watson on Jeopardy, reorganizes the information on incompleteness, and adds information on Konrad Zuse. A distinguished prize-winning logician, Martin Davis has had a career of more than six decades devoted to the important interface between logic and computer science. His expertise, combined with his genuine love of the subject and excellent storytelling, make him the perfect person to tell this story.

Philosophical Explorations of the Legacy of Alan Turing

Author : Juliet Floyd
Publisher : Springer
ISBN 13 : 3319532804
Total Pages : 369 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Philosophical Explorations of the Legacy of Alan Turing by : Juliet Floyd

Download or read book Philosophical Explorations of the Legacy of Alan Turing written by Juliet Floyd and published by Springer. This book was released on 2017-05-30 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chapters “Turing and Free Will: A New Take on an Old Debate” and “Turing and the History of Computer Music” are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Computing Nature

Author : Gordana Dodig-Crnkovic
Publisher : Springer Science & Business Media
ISBN 13 : 3642372252
Total Pages : 268 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Computing Nature by : Gordana Dodig-Crnkovic

Download or read book Computing Nature written by Gordana Dodig-Crnkovic and published by Springer Science & Business Media. This book was released on 2013-03-21 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about nature considered as the totality of physical existence, the universe, and our present day attempts to understand it. If we see the universe as a network of networks of computational processes at many different levels of organization, what can we learn about physics, biology, cognition, social systems, and ecology expressed through interacting networks of elementary particles, atoms, molecules, cells, (and especially neurons when it comes to understanding of cognition and intelligence), organs, organisms and their ecologies? Regarding our computational models of natural phenomena Feynman famously wondered: “Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?” Phenomena themselves occur so quickly and automatically in nature. Can we learn how to harness nature’s computational power as we harness its energy and materials? This volume includes a selection of contributions from the Symposium on Natural Computing/Unconventional Computing and Its Philosophical Significance, organized during the AISB/IACAP World Congress 2012, held in Birmingham, UK, on July 2-6, on the occasion of the centenary of Alan Turing’s birth. In this book, leading researchers investigated questions of computing nature by exploring various facets of computation as we find it in nature: relationships between different levels of computation, cognition with learning and intelligence, mathematical background, relationships to classical Turing computation and Turing’s ideas about computing nature - unorganized machines and morphogenesis. It addresses questions of information, representation and computation, interaction as communication, concurrency and agent models; in short this book presents natural computing and unconventional computing as extension of the idea of computation as symbol manipulation.

Turing's Cathedral

Author : George Dyson
Publisher : Pantheon
ISBN 13 : 0375422773
Total Pages : 466 pages
Book Rating : 4.3/5 (754 download)

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Book Synopsis Turing's Cathedral by : George Dyson

Download or read book Turing's Cathedral written by George Dyson and published by Pantheon. This book was released on 2012 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Documents the innovations of a group of eccentric geniuses who developed computer code in the mid-20th century as part of mathematician Alan Turin's theoretical universal machine idea, exploring how their ideas led to such developments as digital television, modern genetics and the hydrogen bomb.

Engines of Logic

Author : Martin Davis
Publisher : W. W. Norton & Company
ISBN 13 : 9780393322293
Total Pages : 257 pages
Book Rating : 4.3/5 (222 download)

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Book Synopsis Engines of Logic by : Martin Davis

Download or read book Engines of Logic written by Martin Davis and published by W. W. Norton & Company. This book was released on 2001 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: A pioneer in computer development chronicles the history of the machine, and the software that makes it tick, elucidating the core principles driving every calculation, stored record, and mouse click. Originally published as The Universal Computer. Reprint.

Mathletics

Author : Wayne L. Winston
Publisher : Princeton University Press
ISBN 13 : 0691189293
Total Pages : 608 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Mathletics by : Wayne L. Winston

Download or read book Mathletics written by Wayne L. Winston and published by Princeton University Press. This book was released on 2022-02-22 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: How to use math to improve performance and predict outcomes in professional sports Mathletics reveals the mathematical methods top coaches and managers use to evaluate players and improve team performance, and gives math enthusiasts the practical skills they need to enhance their understanding and enjoyment of their favorite sports—and maybe even gain the outside edge to winning bets. This second edition features new data, new players and teams, and new chapters on soccer, e-sports, golf, volleyball, gambling Calcuttas, analysis of camera data, Bayesian inference, ridge regression, and other statistical techniques. After reading Mathletics, you will understand why baseball teams should almost never bunt; why football overtime systems are unfair; why points, rebounds, and assists aren’t enough to determine who’s the NBA’s best player; and more.