Proof In Alonzo Church S And Alan Turing S Mathematical Logic Undecidability Of First Order Logic
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Proof In Alonzo Church S And Alan Turing S Mathematical Logic Undecidability Of First Order Logic
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Author :
language : en
Publisher: Universal-Publishers
Release Date :
Proof In Alonzo Church S And Alan Turing S Mathematical Logic Undecidability Of First Order Logic written by and has been published by Universal-Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Kurt G Del And The Foundations Of Mathematics
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Author : Matthias Baaz
language : en
Publisher: Cambridge University Press
Release Date : 2011-06-06
Kurt G Del And The Foundations Of Mathematics written by Matthias Baaz 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 2011-06-06 with Mathematics categories.
This volume commemorates the life, work and foundational views of Kurt Gödel (1906–78), most famous for his hallmark works on the completeness of first-order logic, the incompleteness of number theory, and the consistency - with the other widely accepted axioms of set theory - of the axiom of choice and of the generalized continuum hypothesis. It explores current research, advances and ideas for future directions not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science. The discussion is supplemented by personal reflections from several scholars who knew Gödel personally, providing some interesting insights into his life. By putting his ideas and life's work into the context of current thinking and perceptions, this book will extend the impact of Gödel's fundamental work in mathematics, logic, philosophy and other disciplines for future generations of researchers.
Alan Turing
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Author : S. Barry Cooper
language : en
Publisher: Elsevier
Release Date : 2013-03-18
Alan Turing written by S. Barry Cooper and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-18 with Mathematics categories.
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
The Encyclopedia Of Philosophy
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Author : Paul Edwards
language : en
Publisher:
Release Date : 1972
The Encyclopedia Of Philosophy written by Paul Edwards and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Philosophy categories.
Treats eastern & western philosophy; it deals with ancient, medieval and modern philosophy; and it discusses the theories of mathematicians, physicist, biologist, sociologists, psychologists, moral reformers and religious thinkers where these have had an impact on philosophy.
On Formally Undecidable Propositions Of Principia Mathematica And Related Systems
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Author : Kurt Gödel
language : en
Publisher: Courier Corporation
Release Date : 1992-01-01
On Formally Undecidable Propositions Of Principia Mathematica And Related Systems written by Kurt Gödel and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
In 1931, a young Austrian mathematician published an epoch-making paper containing one of the most revolutionary ideas in logic since Aristotle. Kurt Giidel maintained, and offered detailed proof, that in any arithmetic system, even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. It is thus uncertain that the basic axioms of arithmetic will not give rise to contradictions. The repercussions of this discovery are still being felt and debated in 20th-century mathematics. The present volume reprints the first English translation of Giidel's far-reaching work. Not only does it make the argument more intelligible, but the introduction contributed by Professor R. B. Braithwaite (Cambridge University}, an excellent work of scholarship in its own right, illuminates it by paraphrasing the major part of the argument. This Dover edition thus makes widely available a superb edition of a classic work of original thought, one that will be of profound interest to mathematicians, logicians and anyone interested in the history of attempts to establish axioms that would provide a rigorous basis for all mathematics. Translated by B. Meltzer, University of Edinburgh. Preface. Introduction by R. B. Braithwaite.
Language In Action
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Author : Johan van Benthem
language : en
Publisher: MIT Press
Release Date : 1995
Language In Action written by Johan van Benthem and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Language Arts & Disciplines categories.
Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. Van Benthem presents the categorial processing of syntax and semantics as a central component in a more general dynamic logic of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities. This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities.
Computability
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Author : B. Jack Copeland
language : en
Publisher: MIT Press
Release Date : 2013-06-07
Computability written by B. Jack Copeland and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-07 with Computers categories.
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
Principles Of Mathematical Logic
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Author : D. Hilbert
language : en
Publisher: American Mathematical Society
Release Date : 2022-05-11
Principles Of Mathematical Logic written by D. Hilbert and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-11 with Mathematics categories.
David Hilbert was particularly interested in the foundations of mathematics. Among many other things, he is famous for his attempt to axiomatize mathematics. This now classic text is his treatment of symbolic logic. This translation is based on the second German edition and has been modified according to the criticisms of Church and Quine. In particular, the authors' original formulation of Gödel's completeness proof for the predicate calculus has been updated. In the first half of the twentieth century, an important debate on the foundations of mathematics took place. Principles of Mathematical Logic represents one of Hilbert's important contributions to that debate. Although symbolic logic has grown considerably in the subsequent decades, this book remains a classic.
Computability Complexity And Languages
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Author : Martin Davis
language : en
Publisher: Elsevier
Release Date : 1994-03-18
Computability Complexity And Languages written by Martin Davis and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-03-18 with Mathematics categories.
Computability, Complexity, and Languages is an introductory text that covers the key areas of computer science, including recursive function theory, formal languages, and automata. It assumes a minimal background in formal mathematics. The book is divided into five parts: Computability, Grammars and Automata, Logic, Complexity, and Unsolvability. - Computability theory is introduced in a manner that makes maximum use of previous programming experience, including a "universal" program that takes up less than a page. - The number of exercises included has more than tripled. - Automata theory, computational logic, and complexity theory are presented in a flexible manner, and can be covered in a variety of different arrangements.
Logic And Discrete Mathematics
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Author : Willem Conradie
language : en
Publisher: John Wiley & Sons
Release Date : 2015-05-08
Logic And Discrete Mathematics written by Willem Conradie 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 2015-05-08 with Mathematics categories.
Solutions manual to accompany Logic and Discrete Mathematics: A Concise Introduction This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in this accompanying solutions manual.