Provability, Computability and Reflection
Author: Lev D. Beklemishev
Publisher: Elsevier
Published: 2000-04-01
Total Pages: 675
ISBN-13: 0080957536
DOWNLOAD EBOOKProvability, Computability and Reflection
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Computability
Author: B. Jack Copeland
Publisher: MIT Press
Published: 2013-06-07
Total Pages: 373
ISBN-13: 0262018993
DOWNLOAD EBOOKComputer 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
Proof and Computation
Author: Helmut Schwichtenberg
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 478
ISBN-13: 3642793614
DOWNLOAD EBOOKLogical concepts and methods are of growing importance in many areas of computer science. The proofs-as-programs paradigm and the wide acceptance of Prolog show this clearly. The logical notion of a formal proof in various constructive systems can be viewed as a very explicit way to describe a computation procedure. Also conversely, the development of logical systems has been influenced by accumulating knowledge on rewriting and unification techniques. This volume contains a series of lectures by leading researchers giving a presentation of new ideas on the impact of the concept of a formal proof on computation theory. The subjects covered are: specification and abstract data types, proving techniques, constructive methods, linear logic, and concurrency and logic.
Functional Analysis
Author: Gerardo Chacón
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2016-12-19
Total Pages: 245
ISBN-13: 3110441926
DOWNLOAD EBOOKThis textbook on functional analysis offers a short and concise introduction to the subject. The book is designed in such a way as to provide a smooth transition between elementary and advanced topics and its modular structure allows for an easy assimilation of the content. Starting from a dedicated chapter on the axiom of choice, subsequent chapters cover Hilbert spaces, linear operators, functionals and duality, Fourier series, Fourier transform, the fixed point theorem, Baire categories, the uniform bounded principle, the open mapping theorem, the closed graph theorem, the Hahn–Banach theorem, adjoint operators, weak topologies and reflexivity, operators in Hilbert spaces, spectral theory of operators in Hilbert spaces, and compactness. Each chapter ends with workable problems. The book is suitable for graduate students, but also for advanced undergraduates, in mathematics and physics. Contents: List of Figures Basic Notation Choice Principles Hilbert Spaces Completeness, Completion and Dimension Linear Operators Functionals and Dual Spaces Fourier Series Fourier Transform Fixed Point Theorem Baire Category Theorem Uniform Boundedness Principle Open Mapping Theorem Closed Graph Theorem Hahn–Banach Theorem The Adjoint Operator Weak Topologies and Reflexivity Operators in Hilbert Spaces Spectral Theory of Operators on Hilbert Spaces Compactness Bibliography Index
Logic, Language, Information, and Computation
Author: Juliette Kennedy
Publisher: Springer
Published: 2017-07-10
Total Pages: 411
ISBN-13: 3662553864
DOWNLOAD EBOOKEdited 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.
Logic, Language, Information, and Computation
Author: Rosalie Iemhoff
Publisher: Springer
Published: 2019-06-23
Total Pages: 683
ISBN-13: 3662595338
DOWNLOAD EBOOKEdited in collaboration with FoLLI, the Association of Logic, Language and Information this book constitutes the refereed proceedings of the 26th Workshop on Logic, Language, Information and Communication, WoLLIC 2019, held in Utrecht, The Netherlands, in July 2019. The 41 full papers together with 6 invited lectures presented were fully reviewed and selected from 60 submissions. The idea is to have a forum which is large enough in the number of possible interactions between logic and the sciences related to information and computation, and yet is small enough to allow for concrete and useful interaction among participants.
Proof And Computation Ii: From Proof Theory And Univalent Mathematics To Program Extraction And Verification
Author: Klaus Mainzer
Publisher: World Scientific
Published: 2021-07-27
Total Pages: 425
ISBN-13: 9811236496
DOWNLOAD EBOOKThis book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes proof theory, constructive mathematics and type theory, univalent mathematics and point-free approaches to topology, extraction of certified programs from proofs, automated proofs in the automotive industry, as well as the philosophical and historical background of proof theory. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.
Analysis, Probability, Applications, and Computation
Author: Karl‐Olof Lindahl
Publisher: Springer
Published: 2019-04-29
Total Pages: 540
ISBN-13: 3030044599
DOWNLOAD EBOOKThis book is a collection of short papers from the 11th International ISAAC Congress 2017 in Växjö, Sweden. The papers, written by the best international experts, are devoted to recent results in mathematics with a focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on the current research in mathematical analysis and its various interdisciplinary applications.
Interactive Theorem Proving and Program Development
Author: Yves Bertot
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 492
ISBN-13: 366207964X
DOWNLOAD EBOOKA 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.
Theory and Applications of Models of Computation
Author: Manindra Agrawal
Publisher: Springer Science & Business Media
Published: 2008-04-08
Total Pages: 610
ISBN-13: 3540792279
DOWNLOAD EBOOKThis book constitutes the refereed proceedings of the 5th International Conference on Theory and Applications of Models of Computation, TAMC 2008, held in Xi'an, China in April 2008. The 48 revised full papers presented together with 2 invited talks and 1 plenary lecture were carefully reviewed and selected from 192 submissions. The papers address current issues of all major areas in computer science, mathematics (especially logic) and the physical sciences - computation, algorithms, complexity and computability theory in particular. With this crossdisciplinary character the conference is given a special flavor and distinction.
