Download or read book Provability Computability and Reflection written by Lev D. Beklemishev and published by Elsevier. This book was released on 2009-06-15 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection

Download or read book Provability Computability and Reflection written by Lev D. Beklemishev and published by Elsevier Science. This book was released on 2000-04-01 with total page 89 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection

Download or read book Provability Computability and Reflection written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection

Download or read book Foundational Studies written by Andrzej Mostowski and published by Elsevier. This book was released on 1979 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection.

Download or read book Computability written by B. Jack Copeland and published by MIT Press. This book was released on 2015-01-30 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. Contributors Scott 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

Download or read book Logic Language Information and Computation written by Juliette Kennedy and published by Springer. This book was released on 2017-07-10 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 24th Workshop on Logic, Language, Information and Communication, WoLLIC 2017, held in London, UK, in August 2017. The 28 contributed papers were carefully reviewed and selected from 61 submissions. They cover interdisciplinary research in pure and applied logic, aiming at interactions between logic and the sciences related to information and computation.

Download or read book Logic Language and Computation written by Nick Bezhanishvili and published by Springer Science & Business Media. This book was released on 2011-07-18 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this book constitutes the refereed proceedings of the 8th International Tbilisi Symposium on Logic, Language, and Computation, TbiLLC 2009, held in Bakuriani, Georgia, in September 2009. The 20 revised full papers included in the book were carefully reviewed and selected from numerous presentations given at the symposium. The focus of the papers is on the following topics: natural language syntax, semantics, and pragmatics; constructive, modal and algebraic logic; linguistic typology and semantic universals; logics for artificial intelligence; information retrieval, query answer systems; logic, games, and formal pragmatics; language evolution and learnability; computational social choice; historical linguistics, history of logic.

Download or read book Computability and Logic written by George S. Boolos and published by Cambridge University Press. This book was released on 2007-09-17 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fifth edition of 'Computability and Logic' covers not just the staple topics of an intermediate logic course such as Godel's incompleteness theorems, but also optional topics that include Turing's theory of computability and Ramsey's theorem.

Download or read book Turing s Revolution written by Giovanni Sommaruga and published by Birkhäuser. This book was released on 2016-01-21 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the confluence of ideas in Turing’s era and work and examines the impact of his work on mathematical logic and theoretical computer science. It combines contributions by well-known scientists on the history and philosophy of computability theory as well as on generalised Turing computability. By looking at the roots and at the philosophical and technical influence of Turing’s work, it is possible to gather new perspectives and new research topics which might be considered as a continuation of Turing’s working ideas well into the 21st century.

Download or read book Interactive Theorem Proving and Program Development written by Yves Bertot and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical introduction to the development of proofs and certified programs using Coq. An invaluable tool for researchers, students, and engineers interested in formal methods and the development of zero-fault software.

Download or read book Mathematical Problems from Applied Logic II written by Dov Gabbay and published by Springer Science & Business Media. This book was released on 2007-07-28 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions from world-renowned logicians, discussing important topics of logic from the point of view of their further development in light of requirements arising from successful application in Computer Science and AI language. Coverage includes: the logic of provability, computability theory applied to biology, psychology, physics, chemistry, economics, and other basic sciences; computability theory and computable models; logic and space-time geometry; hybrid systems; logic and region-based theory of space.

Download or read book Artificial and Mathematical Theory of Computation written by Vladimir Lifschitz and published by Academic Press. This book was released on 2012-12-02 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Artificial and Mathematical Theory of Computation is a collection of papers that discusses the technical, historical, and philosophical problems related to artificial intelligence and the mathematical theory of computation. Papers cover the logical approach to artificial intelligence; knowledge representation and common sense reasoning; automated deduction; logic programming; nonmonotonic reasoning and circumscription. One paper suggests that the design of parallel programming languages will invariably become more sophisticated as human skill in programming and software developments improves to attain faster running programs. An example of metaprogramming to systems concerns the design and control of operations of factory devices, such as robots and numerically controlled machine tools. Metaprogramming involves two design aspects: that of the activity of a single device and that of the interaction with other devices. One paper cites the application of artificial intelligence pertaining to the project "proof checker for first-order logic" at the Stanford Artificial Intelligence Laboratory. Another paper explains why the bisection algorithm widely used in computer science does not work. This book can prove valuable to engineers and researchers of electrical, computer, and mechanical engineering, as well as, for computer programmers and designers of industrial processes.

Download or read book Deduction Computation Experiment written by Rossella Lupacchini and published by Springer Science & Business Media. This book was released on 2008-09-25 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Provability Computability and Reflection written by Lev D. Beklemishev and published by Elsevier Science. This book was released on 2000-04-01 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection

Download or read book Computability in Analysis and Physics written by Marian B. Pour-El and published by Cambridge University Press. This book was released on 2017-03-02 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning.

Download or read book Constructive Order Types written by John N. Crossley and published by . This book was released on 1969 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection.

Download or read book Gentzen s Centenary written by Reinhard Kahle and published by Springer. This book was released on 2015-11-02 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They underlie modern developments in computer science such as automated theorem proving and type theory.