Applied Proof Theory Proof Interpretations And Their Use In Mathematics

Author : Ulrich Kohlenbach
Publisher : Springer Science & Business Media
ISBN 13 : 3540775331
Total Pages : 539 pages
Book Rating : 4.31/5 ( download)

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Download or read book Applied Proof Theory: Proof Interpretations and their Use in Mathematics written by Ulrich Kohlenbach and published by Springer Science & Business Media. This book was released on 2008-05-23 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Toshiyasu Arai
Publisher : Springer Nature
ISBN 13 : 9811564590
Total Pages : 327 pages
Book Rating : 4.98/5 ( download)

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Download or read book Ordinal Analysis with an Introduction to Proof Theory written by Toshiyasu Arai and published by Springer Nature. This book was released on 2020-08-11 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides readers with a guide to both ordinal analysis, and to proof theory. It mainly focuses on ordinal analysis, a research topic in proof theory that is concerned with the ordinal theoretic content of formal theories. However, the book also addresses ordinal analysis and basic materials in proof theory of first-order or omega logic, presenting some new results and new proofs of known ones.Primarily intended for graduate students and researchers in mathematics, especially in mathematical logic, the book also includes numerous exercises and answers for selected exercises, designed to help readers grasp and apply the main results and techniques discussed.

Author : Sara Negri
Publisher : Cambridge University Press
ISBN 13 : 1139501526
Total Pages : 279 pages
Book Rating : 4.21/5 ( download)

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Download or read book Proof Analysis written by Sara Negri and published by Cambridge University Press. This book was released on 2011-09-29 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book continues from where the authors' previous book, Structural Proof Theory, ended. It presents an extension of the methods of analysis of proofs in pure logic to elementary axiomatic systems and to what is known as philosophical logic. A self-contained brief introduction to the proof theory of pure logic is included that serves both the mathematically and philosophically oriented reader. The method is built up gradually, with examples drawn from theories of order, lattice theory and elementary geometry. The aim is, in each of the examples, to help the reader grasp the combinatorial behaviour of an axiom system, which typically leads to decidability results. The last part presents, as an application and extension of all that precedes it, a proof-theoretical approach to the Kripke semantics of modal and related logics, with a great number of new results, providing essential reading for mathematical and philosophical logicians.

Author : Françoise Delon
Publisher : Cambridge University Press
ISBN 13 : 1139488937
Total Pages : 282 pages
Book Rating : 4.38/5 ( download)

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Download or read book Logic Colloquium 2007 written by Françoise Delon and published by Cambridge University Press. This book was released on 2010-06-07 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium, is among the most prestigious annual meetings in the field. The current volume, Logic Colloquium 2007, with contributions from plenary speakers and selected special session speakers, contains both expository and research papers by some of the best logicians in the world. This volume covers many areas of contemporary logic: model theory, proof theory, set theory, and computer science, as well as philosophical logic, including tutorials on cardinal arithmetic, on Pillay's conjecture, and on automatic structures. This volume will be invaluable for experts as well as those interested in an overview of central contemporary themes in mathematical logic.

Author : George Metcalfe
Publisher : Springer Science & Business Media
ISBN 13 : 1402094094
Total Pages : 279 pages
Book Rating : 4.95/5 ( download)

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Download or read book Proof Theory for Fuzzy Logics written by George Metcalfe and published by Springer Science & Business Media. This book was released on 2008-11-27 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems (including key standard completeness results) and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations.

Author : Sven Ove Hansson
Publisher : Springer
ISBN 13 : 3319774344
Total Pages : 733 pages
Book Rating : 4.43/5 ( download)

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Download or read book Introduction to Formal Philosophy written by Sven Ove Hansson and published by Springer. This book was released on 2018-10-24 with total page 733 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Undergraduate Textbook introduces key methods and examines the major areas of philosophy in which formal methods play pivotal roles. Coverage begins with a thorough introduction to formalization and to the advantages and pitfalls of formal methods in philosophy. The ensuing chapters show how to use formal methods in a wide range of areas. Throughout, the contributors clarify the relationships and interdependencies between formal and informal notions and constructions. Their main focus is to show how formal treatments of philosophical problems may help us understand them better. Formal methods can be used to solve problems but also to express new philosophical problems that would never have seen the light of day without the expressive power of the formal apparatus. ​Formal philosophy merges work in different areas of philosophy as well as logic, mathematics, computer science, linguistics, physics, psychology, biology, economics, political theory, and sociology. This title offers an accessible introduction to this new interdisciplinary research area to a wide academic audience.

Author : Matthias Baaz
Publisher : Cambridge University Press
ISBN 13 : 1139498436
Total Pages : 541 pages
Book Rating : 4.32/5 ( download)

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Download or read book Kurt Gödel and the Foundations of Mathematics written by Matthias Baaz and published by Cambridge University Press. This book was released on 2011-06-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Mainzer Klaus
Publisher : World Scientific
ISBN 13 : 9813270950
Total Pages : 300 pages
Book Rating : 4.54/5 ( download)

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Download or read book Proof And Computation: Digitization In Mathematics, Computer Science And Philosophy written by Mainzer Klaus and published by World Scientific. This book was released on 2018-05-30 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents: Proof and Computation (K Mainzer) Constructive Convex Programming (J Berger and G Svindland) Exploring Predicativity (L Crosilla) Constructive Functional Analysis: An Introduction (H Ishihara) Program Extraction (K Miyamoto) The Data Structures of the Lambda Terms (M Sato) Provable (and Unprovable) Computability (S Wainer) Introduction to Minlog (F Wiesnet) Readership: Graduate students, researchers, and professionals in Mathematics and Computer Science. Keywords: Proof Theory;Computability Theory;Program Extraction;Constructive Analysis;PredicativityReview: Key Features: This book gathers recent contributions of distinguished experts It makes emerging fields accessible to a wider audience, appealing to a broad readership with diverse backgrounds It fills a gap between (under-)graduate level textbooks and state-of-the-art research papers

Author : Reinhard Kahle
Publisher : Springer
ISBN 13 : 331910103X
Total Pages : 561 pages
Book Rating : 4.33/5 ( download)

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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.

Author : S.R. Buss
Publisher : Elsevier
ISBN 13 : 0080533183
Total Pages : 823 pages
Book Rating : 4.86/5 ( download)

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Download or read book Handbook of Proof Theory written by S.R. Buss and published by Elsevier. This book was released on 1998-07-09 with total page 823 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.