Applied Proof Theory Proof Interpretations And Their Use In Mathematics
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Applied Proof Theory Proof Interpretations And Their Use In Mathematics
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Author : Ulrich Kohlenbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-23
Applied Proof Theory Proof Interpretations And Their Use In Mathematics written by Ulrich Kohlenbach and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-23 with Mathematics categories.
This is the first treatment in book format of proof-theoretic transformations - known as proof interpretations - that focuses on applications to ordinary mathematics. It covers both the necessary logical machinery behind the proof interpretations that are used in recent applications as well as – via extended case studies – carrying out some of these applications in full detail. This subject has historical roots in the 1950s. This book for the first time tells the whole story.
Logic Language Information And Computation
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Author : Rosalie Iemhoff
language : en
Publisher: Springer
Release Date : 2019-06-23
Logic Language Information And Computation written by Rosalie Iemhoff and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-23 with Computers categories.
Edited 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.
Artificial Intelligence When Do Machines Take Over
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Author : Klaus Mainzer
language : en
Publisher: Springer Nature
Release Date : 2019-10-14
Artificial Intelligence When Do Machines Take Over written by Klaus Mainzer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-14 with Technology & Engineering categories.
Everybody knows them. Smartphones that talk to us, wristwatches that record our health data, workflows that organize themselves automatically, cars, airplanes and drones that control themselves, traffic and energy systems with autonomous logistics or robots that explore distant planets are technical examples of a networked world of intelligent systems. Machine learning is dramatically changing our civilization. We rely more and more on efficient algorithms, because otherwise we will not be able to cope with the complexity of our civilizing infrastructure. But how secure are AI algorithms? This challenge is taken up in the 2nd edition: Complex neural networks are fed and trained with huge amounts of data (big data). The number of necessary parameters explodes exponentially. Nobody knows exactly what is going on in these "black boxes". In machine learning we need more explainability and accountability of causes and effects in order to be able to decide ethical and legal questions of responsibility (e.g. in autonomous driving or medicine)! Besides causal learning, we also analyze procedures of tests and verification to get certified AI-programs. Since its inception, AI research has been associated with great visions of the future of mankind. It is already a key technology that will decide the global competition of social systems. "Artificial Intelligence and Responsibility" is another central supplement to the 2nd edition: How should we secure our individual liberty rights in the AI world? This book is a plea for technology design: AI must prove itself as a service in society.
Approximate Fixed Points Of Nonexpansive Mappings
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Author : Alexander J. Zaslavski
language : en
Publisher: Springer Nature
Release Date : 2024-09-25
Approximate Fixed Points Of Nonexpansive Mappings written by Alexander J. Zaslavski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-25 with Mathematics categories.
Fixed point theory of nonlinear operators has been a rapidly growing area of research and plays an important role in the study of variational inequalities, monotone operators, feasibility problems, and optimization theory, to name just several. This book discusses iteration processes associated with a given nonlinear mapping which generate its approximate fixed point and in some cases converge to a fixed point of the mapping. Various classes of nonlinear single-valued and set-valued mappings are considered along with iteration processes under the presence of computational errors. Of particular interest to mathematicians working in fixed point theory and nonlinear analysis, the added value for the reader are the solutions presented to a number of difficult problems in the fixed point theory which have important applications.
Convex Analysis And Optimization In Hadamard Spaces
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Author : Miroslav Bacak
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-10-29
Convex Analysis And Optimization In Hadamard Spaces written by Miroslav Bacak and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-29 with Mathematics categories.
In the past two decades, convex analysis and optimization have been developed in Hadamard spaces. This book represents a first attempt to give a systematic account on the subject. Hadamard spaces are complete geodesic spaces of nonpositive curvature. They include Hilbert spaces, Hadamard manifolds, Euclidean buildings and many other important spaces. While the role of Hadamard spaces in geometry and geometric group theory has been studied for a long time, first analytical results appeared as late as in the 1990s. Remarkably, it turns out that Hadamard spaces are appropriate for the theory of convex sets and convex functions outside of linear spaces. Since convexity underpins a large number of results in the geometry of Hadamard spaces, we believe that its systematic study is of substantial interest. Optimization methods then address various computational issues and provide us with approximation algorithms which may be useful in sciences and engineering. We present a detailed description of such an application to computational phylogenetics. The book is primarily aimed at both graduate students and researchers in analysis and optimization, but it is accessible to advanced undergraduate students as well.
Programming Languages And Systems
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Author : Bor-Yuh Evan Chang
language : en
Publisher: Springer
Release Date : 2017-11-17
Programming Languages And Systems written by Bor-Yuh Evan Chang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-17 with Computers categories.
This book constitutes the proceedings of the 15th Asian Symposium on Programming Languages and Systems, APLAS 2017, held in Suzhou, China, in November 2017. The 24 papers presented in this volume were carefully reviewed and selected from 56 submissions. They were organized in topical sections named: security; heap and equivalence reasoning; concurrency and verification; domain-specific languages; semantics; and numerical reasoning. The volume also contains two invited talks in full-paper length.
Beyond The Horizon Of Computability
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Author : Marcella Anselmo
language : en
Publisher: Springer Nature
Release Date : 2020-06-23
Beyond The Horizon Of Computability written by Marcella Anselmo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-23 with Computers categories.
This book constitutes the proceedings of the 16th Conference on Computability in Europe, CiE 2020, which was planned to be held in Fisciano, Italy, during June 29 until July 3, 2020. The conference moved to a virtual format due to the coronavirus pandemic. The 30 full and 5 short papers presented in this volume were carefully reviewed and selected from 72 submissions. CiE promotes the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences, such as physics and biology, as well as related fields, such as philosophy and history of computing. CiE 2020 had as its motto Beyond the Horizon of Computability, reflecting the interest of CiE in research transgressing the traditional boundaries of computability theory.
Reverse Mathematics
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Author : Damir D. Dzhafarov
language : en
Publisher: Springer Nature
Release Date : 2022-07-25
Reverse Mathematics written by Damir D. Dzhafarov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-25 with Computers categories.
Reverse mathematics studies the complexity of proving mathematical theorems and solving mathematical problems. Typical questions include: Can we prove this result without first proving that one? Can a computer solve this problem? A highly active part of mathematical logic and computability theory, the subject offers beautiful results as well as significant foundational insights. This text provides a modern treatment of reverse mathematics that combines computability theoretic reductions and proofs in formal arithmetic to measure the complexity of theorems and problems from all areas of mathematics. It includes detailed introductions to techniques from computable mathematics, Weihrauch style analysis, and other parts of computability that have become integral to research in the field. Topics and features: Provides a complete introduction to reverse mathematics, including necessary background from computability theory, second order arithmetic, forcing, induction, and model construction Offers a comprehensive treatment of the reverse mathematics of combinatorics, including Ramsey's theorem, Hindman's theorem, and many other results Provides central results and methods from the past two decades, appearing in book form for the first time and including preservation techniques and applications of probabilistic arguments Includes a large number of exercises of varying levels of difficulty, supplementing each chapter The text will be accessible to students with a standard first year course in mathematical logic. It will also be a useful reference for researchers in reverse mathematics, computability theory, proof theory, and related areas. Damir D. Dzhafarov is an Associate Professor of Mathematics at the University of Connecticut, CT, USA. Carl Mummert is a Professor of Computer and Information Technology at Marshall University, WV, USA.
Proof And Computation Digitization In Mathematics Computer Science And Philosophy
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Author : Klaus Mainzer
language : en
Publisher: World Scientific
Release Date : 2018-05-30
Proof And Computation Digitization In Mathematics Computer Science And Philosophy written by Klaus Mainzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-30 with Mathematics categories.
This 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 Predicative Foundations, Constructive Mathematics and Type Theory, Computation in Higher Types, Extraction of Programs from Proofs, and Algorithmic Aspects in Financial Mathematics. 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.
Formalism And Beyond
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Author : Godehard Link
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2014-10-09
Formalism And Beyond written by Godehard Link and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-09 with Philosophy categories.
The essays collected in this volume focus on the role of formalist aspects in mathematical theorizing and practice, examining issues such as infinity, finiteness, and proof procedures, as well as central historical figures in the field, including Frege, Russell, Hilbert and Wittgenstein. Using modern logico-philosophical tools and systematic conceptual and logical analyses, the volume provides a thorough, up-to-date account of the subject.