Proofs And Computations

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Proofs And Computations

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Author : Helmut Schwichtenberg
language : en
Publisher: Cambridge University Press
Release Date : 2011-12-15

Proofs And Computations written by Helmut Schwichtenberg 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 2011-12-15 with Mathematics categories.

Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.

Proof And Computation

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Author : Helmut Schwichtenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Proof And Computation written by Helmut Schwichtenberg 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 2012-12-06 with Computers categories.

Logical 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.

Proof And Computation Ii From Proof Theory And Univalent Mathematics To Program Extraction And Verification

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Author : Klaus Mainzer
language : en
Publisher: World Scientific
Release Date : 2021-07-27

Proof And Computation Ii From Proof Theory And Univalent Mathematics To Program Extraction And Verification 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 2021-07-27 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 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.

Complexity Of Computations And Proofs

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Author : Jan Krajíček
language : en
Publisher:
Release Date : 2003

Complexity Of Computations And Proofs written by Jan Krajíček and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

Handbook Of Logic In Artificial Intelligence And Logic Programming Volume 5 Logic Programming

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Author : Dov M. Gabbay
language : en
Publisher: Clarendon Press
Release Date : 1998-01-08

Handbook Of Logic In Artificial Intelligence And Logic Programming Volume 5 Logic Programming written by Dov M. Gabbay and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-08 with Computers categories.

The Handbook of Logic in Artificial Intelligence and Logic Programming is a multi-volume work covering all major areas of the application of logic to artificial intelligence and logic programming. The authors are chosen on an international basis and are leaders in the fields covered. Volume 5 is the last in this well-regarded series. Logic is now widely recognized as one of the foundational disciplines of computing. It has found applications in virtually all aspects of the subject, from software and hardware engineering to programming languages and artificial intelligence. In response to the growing need for an in-depth survey of these applications the Handbook of Logic in Artificial Intelligence and its companion, the Handbook of Logic in Computer Science have been created. The Handbooks are a combination of authoritative exposition, comprehensive survey, and fundamental research exploring the underlying themes in the various areas. Some mathematical background is assumed, and much of the material will be of interest to logicians and mathematicians. Volume 5 focuses particularly on logic programming. The chapters, which in many cases are of monograph length and scope, emphasize possible unifying themes.

Computational Aspects Of Linear Logic

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Author : Patrick Lincoln
language : en
Publisher:
Release Date : 1992

Computational Aspects Of Linear Logic written by Patrick Lincoln and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Logic, Symbolic and mathematical categories.

Mathematical Knowledge Management

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Author : Jonathan M. Borwein
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-26

Mathematical Knowledge Management written by Jonathan M. Borwein 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 2006-07-26 with Computers categories.

Constitutes the proceedings of the 5th International Conference on Mathematical Knowledge Management, MKM 2006, held in Wokingham. This book includes 22 full papers which cover the whole area of mathematical knowledge management in the intersection of mathematics, computer science, library science, and scientific publishing.

Proofs For All Mathematical Calculations

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Author : Louis Traub
language : en
Publisher:
Release Date : 1914

Proofs For All Mathematical Calculations written by Louis Traub and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1914 with Ready-reckoners categories.

Deduction Computation Experiment

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Author : Rossella Lupacchini
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-25

Deduction Computation Experiment written by Rossella Lupacchini 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 2008-09-25 with Philosophy categories.

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.

Automata Languages And Programming

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Author :
language : en
Publisher:
Release Date : 2004

Automata Languages And Programming written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Computer programming categories.