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Author : N. Shankar
Publisher : Cambridge University Press
Page : 224 pages
File Size : 41,5 Mb
Release : 1997-01-30
Category : Computers
ISBN : 0521585333
Describes the use of computer programs to check several proofs in the foundations of mathematics.
Author : Ernest Nagel,James R. Newman
Publisher : Lulu.com
Page : 132 pages
File Size : 44,5 Mb
Release : 2018-09-14
Category : Gödel's theorem
ISBN : 9780359079261
In 1931 Kurt Gödel published his paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." Gödel’s paper challenged certain basic assumptions underlying much research in mathematics and logic. However, few scholars were unable to understand Gödel’s ideas. Ernest Nagel and James Newman provide a readable and accessible explanation of the main ideas and broad implications of Gödel's discovery.
Author : Ernest Nagel,James R. Newman
Publisher : Unknown
Page : 118 pages
File Size : 55,6 Mb
Release : 1971
Category : Electronic
ISBN : OCLC:637854140
Author : Roman Murawski
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 47,6 Mb
Release : 2013-03-14
Category : Philosophy
ISBN : 9789401728669
Recursive Functions and Metamathematics deals with problems of the completeness and decidability of theories, using as its main tool the theory of recursive functions. This theory is first introduced and discussed. Then Gödel's incompleteness theorems are presented, together with generalizations, strengthenings, and the decidability theory. The book also considers the historical and philosophical context of these issues and their philosophical and methodological consequences. Recent results and trends have been included, such as undecidable sentences of mathematical content, reverse mathematics. All the main results are presented in detail. The book is self-contained and presupposes only some knowledge of elementary mathematical logic. There is an extensive bibliography. Readership: Scholars and advanced students of logic, mathematics, philosophy of science.
Author : Ernest Nagel,James R Newman,Douglas R. Hofstadter
Publisher : NYU Press
Page : 163 pages
File Size : 47,5 Mb
Release : 2001-10-01
Category : Mathematics
ISBN : 9780814758014
An accessible explanation of Kurt Gödel's groundbreaking work in mathematical logic In 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times." However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject. New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.
Author : ERNEST. NAGEL
Publisher : Unknown
Page : 0 pages
File Size : 54,9 Mb
Release : 2018
Category : Electronic
ISBN : 1033002089
Author : Gregory J. Chaitin
Publisher : Springer Science & Business Media
Page : 148 pages
File Size : 52,5 Mb
Release : 1999-07-01
Category : Mathematics
ISBN : 9814021725
This essential companion to Chaitins highly successful The Limits of Mathematics, gives a brilliant historical survey of important work on the foundations of mathematics. The Unknowable is a very readable introduction to Chaitins ideas, and includes software (on the authors website) that will enable users to interact with the authors proofs. "Chaitins new book, The Unknowable, is a welcome addition to his oeuvre. In it he manages to bring his amazingly seminal insights to the attention of a much larger audience His work has deserved such treatment for a long time." JOHN ALLEN PAULOS, AUTHOR OF ONCE UPON A NUMBER
Author : Donald MacKenzie
Publisher : MIT Press
Page : 448 pages
File Size : 48,6 Mb
Release : 2004-01-30
Category : Social Science
ISBN : 0262632950
Most aspects of our private and social lives—our safety, the integrity of the financial system, the functioning of utilities and other services, and national security—now depend on computing. But how can we know that this computing is trustworthy? In Mechanizing Proof, Donald MacKenzie addresses this key issue by investigating the interrelations of computing, risk, and mathematical proof over the last half century from the perspectives of history and sociology. His discussion draws on the technical literature of computer science and artificial intelligence and on extensive interviews with participants. MacKenzie argues that our culture now contains two ideals of proof: proof as traditionally conducted by human mathematicians, and formal, mechanized proof. He describes the systems constructed by those committed to the latter ideal and the many questions those systems raise about the nature of proof. He looks at the primary social influence on the development of automated proof—the need to predict the behavior of the computer systems upon which human life and security depend—and explores the involvement of powerful organizations such as the National Security Agency. He concludes that in mechanizing proof, and in pursuing dependable computer systems, we do not obviate the need for trust in our collective human judgment.
Author : Bernd Finkbeiner,Geguang Pu,Lijun Zhang
Publisher : Springer
Page : 520 pages
File Size : 44,8 Mb
Release : 2015-10-07
Category : Computers
ISBN : 9783319249537
This book constitutes the proceedings of the 13th International Symposium on Automated Technology for Verification and Analysis, ATVA 2015, held in Shanghai, China, in October 2015. The 27 revised papers presented together with 6 tool papers in this volume were carefully reviewed and selected from 95 submissions. They show current research on theoretical and practical aspects of automated analysis, verification and synthesis by providing an international forum for interaction among the researchers in academia and industry.
Author : Alexandra Pavlova,Mina Young Pedersen,Raffaella Bernardi
Publisher : Springer Nature
Page : 236 pages
File Size : 44,9 Mb
Release : 2024-01-28
Category : Computers
ISBN : 9783031506284
The European Summer School in Logic, Language and Information (ESSLLI) is organized every year by the Association for Logic, Language and Information (FoLLI) in different sites around Europe. The papers cover vastly dierent topics, but each fall in the intersection of the three primary topics of ESSLLI: Logic, Language and Computation. The 13 papers presented in this volume have been selected among 81 submitted papers over the years 2019, 2020 and 2021. The ESSLLI Student Session is an excellent venue for students to present their work and receive valuable feedback from renowned experts in their respective fields. The Student Session accepts submissions for three different tracks: Language and Computation (LaCo), Logic and Computation (LoCo), and Logic and Language (LoLa).
Author : Jaime Simão Sichman,Julian Padget,Sascha Ossowski,Pablo Noriega
Publisher : Springer
Page : 331 pages
File Size : 40,7 Mb
Release : 2008-03-21
Category : Computers
ISBN : 9783540790037
This book constitutes the refereed post-workshop proceedings of the International Workshop on Coordination, Organization, Institutions and Norms in Agent Systems, COIN 2007. The 23 papers in this volume were carefully selected from 38 initial submissions.
Author : Rossella Lupacchini,Giovanna Corsi
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 55,8 Mb
Release : 2008-09-25
Category : Philosophy
ISBN : 9788847007840
This volume is located in a cross-disciplinary ?eld bringing together mat- matics, logic, natural science and philosophy. Re?ection on the e?ectiveness of proof brings out a number of questions that have always been latent in the informal understanding of the subject. What makes a symbolic constr- tion signi?cant? What makes an assumption reasonable? What makes a proof reliable? G ̈ odel, Church and Turing, in di?erent ways, achieve a deep und- standing of the notion of e?ective calculability involved in the nature of proof. Turing’s work in particular provides a “precise and unquestionably adequate” de?nition of the general notion of a formal system in terms of a machine with a ?nite number of parts. On the other hand, Eugene Wigner refers to the - reasonable e?ectiveness of mathematics in the natural sciences as a miracle. Where should the boundary be traced between mathematical procedures and physical processes? What is the characteristic use of a proof as a com- tation, as opposed to its use as an experiment? What does natural science tell us about the e?ectiveness of proof? What is the role of mathematical proofs in the discovery and validation of empirical theories? The papers collected in this book are intended to search for some answers, to discuss conceptual and logical issues underlying such questions and, perhaps, to call attention to other relevant questions.
Author : Ulrich Berger,Helmut Schwichtenberg
Publisher : Springer Science & Business Media
Page : 451 pages
File Size : 42,8 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642586224
Recent developments in computer science clearly show the need for a better theoretical foundation for some central issues. Methods and results from mathematical logic, in particular proof theory and model theory, are of great help here and will be used much more in future than previously. This book provides an excellent introduction to the interplay of mathematical logic and computer science. It contains extensively reworked versions of the lectures given at the 1997 Marktoberdorf Summer School by leading researchers in the field. Topics covered include: proof theory and specification of computation (J.-Y. Girard, D. Miller), complexity of proofs and programs (S. R. Buss, S. S. Wainer), computational content of proofs (H. Schwichtenberg), constructive type theory (P. Aczel, H. Barendregt, R. L. Constable), computational mathematics, (U. Martin), rewriting logic (J. Meseguer), and game semantics (S. Abramski).
Author : Pascal Fontaine
Publisher : Springer Nature
Page : 603 pages
File Size : 53,5 Mb
Release : 2019-08-20
Category : Computers
ISBN : 9783030294366
This book constitutes the proceeding of the 27th International Conference on Automated Deduction, CADE 27, held in Natal, Brazil, in August 2019. The 27 full papers and 7 system descriptions presented were carefully reviewed and selected from 65 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience.
Author : A. S. Troelstra,H. Schwichtenberg
Publisher : Cambridge University Press
Page : 436 pages
File Size : 40,9 Mb
Release : 2000-07-27
Category : Computers
ISBN : 0521779111
This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.
