The Legacy Of Kurt Schütte

Author : Reinhard Kahle,Michael Rathjen
Publisher : Springer Nature
Page : 502 pages
File Size : 50,5 Mb
Release : 2020-08-10
Category : Mathematics
ISBN : 9783030494247

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The Legacy of Kurt Schütte by Reinhard Kahle,Michael Rathjen Pdf

This book on proof theory centers around the legacy of Kurt Schütte and its current impact on the subject. Schütte was the last doctoral student of David Hilbert who was the first to see that proofs can be viewed as structured mathematical objects amenable to investigation by mathematical methods (metamathematics). Schütte inaugurated the important paradigm shift from finite proofs to infinite proofs and developed the mathematical tools for their analysis. Infinitary proof theory flourished in his hands in the 1960s, culminating in the famous bound Γ0 for the limit of predicative mathematics (a fame shared with Feferman). Later his interests shifted to developing infinite proof calculi for impredicative theories. Schütte had a keen interest in advancing ordinal analysis to ever stronger theories and was still working on some of the strongest systems in his eighties. The articles in this volume from leading experts close to his research, show the enduring influence of his work in modern proof theory. They range from eye witness accounts of his scientific life to developments at the current research frontier, including papers by Schütte himself that have never been published before.

Author : Fernando Ferreira,Reinhard Kahle,Giovanni Sommaruga
Publisher : Springer Nature
Page : 293 pages
File Size : 54,7 Mb
Release : 2022-09-17
Category : Mathematics
ISBN : 9783030777999

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Axiomatic Thinking II by Fernando Ferreira,Reinhard Kahle,Giovanni Sommaruga Pdf

In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere. The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come. The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations.

Author : Gerhard Heinzmann,Gereon Wolters
Publisher : Springer Nature
Page : 268 pages
File Size : 48,5 Mb
Release : 2021-08-17
Category : Mathematics
ISBN : 9783030658243

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Paul Lorenzen -- Mathematician and Logician by Gerhard Heinzmann,Gereon Wolters Pdf

This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics. The papers also explore how practitioners can implement Lorenzen’s systematical ideas in today’s debates on proof-theoretic semantics, databank management, and stochastics. Coverage details key contributions of Lorenzen to constructive mathematics, Lorenzen’s work on lattice-groups and divisibility theory, and modern set theory and Lorenzen’s critique of actual infinity. The contributors also look at the main problem of Grundlagenforschung and Lorenzen’s consistency proof and Hilbert’s larger program. In addition, the papers offer a constructive examination of a Russell-style Ramified Type Theory and a way out of the circularity puzzle within the operative justification of logic and mathematics. Paul Lorenzen's name is associated with the Erlangen School of Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of science determined philosophical discussions especially in Germany in the 1960s and 1970s. This volume features 10 papers from a meeting that took place at the University of Konstanz.

Author : Renate A. Schmidt,Cláudia Nalon
Publisher : Springer
Page : 381 pages
File Size : 51,7 Mb
Release : 2017-09-04
Category : Computers
ISBN : 9783319669021

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Automated Reasoning with Analytic Tableaux and Related Methods by Renate A. Schmidt,Cláudia Nalon Pdf

This book contains the proceedings of the 26th International Conference on Automated Reasoning with Analytics Tableaux and Related Methods, TABLEAUX 2017, held in Brasília, Bazil, in September 2017. The 19 contributed papers presented in this volume were carefully reviewed and selected from 27 submissions.They are organized in topical sections named: Sequent systems; tableaux; transitive closure and cyclic proofs; formalization and complexity. Also included are papers of three invited speakers.

Author : Revantha Ramanayake,Josef Urban
Publisher : Springer Nature
Page : 487 pages
File Size : 48,6 Mb
Release : 2023-10-15
Category : Computers
ISBN : 9783031435133

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Automated Reasoning with Analytic Tableaux and Related Methods by Revantha Ramanayake,Josef Urban Pdf

This open access book constitutes the proceedings of the proceedings of the 32nd International Conference on Automated Reasoning with Analytic Tableaux and Related Methods, TABLEAUX 2023, held in Prague, Czech Republic, during September 18-21, 2023. The 20 full papers and 5 short papers included in this book together with 5 abstracts of invited talks were carefully reviewed and selected from 43 submissions. They present research on all aspects of the mechanization of reasoning with tableaux and related methods. The papers are organized in the following topical sections: tableau calculi; sequent calculi; theorem proving; non-wellfounded proofs; modal logics; linear logic and MV-algebras; separation logic; and first-order logics.

Author : André Platzer
Publisher : Springer Nature
Page : 655 pages
File Size : 46,5 Mb
Release : 2021
Category : Artificial intelligence
ISBN : 9783030798765

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Automated Deduction - CADE 28 by André Platzer Pdf

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions.

Author : Peter M. Schuster,Monika Seisenberger,Andreas Weiermann
Publisher : Springer Nature
Page : 391 pages
File Size : 49,7 Mb
Release : 2020-01-01
Category : Philosophy
ISBN : 9783030302290

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Well-Quasi Orders in Computation, Logic, Language and Reasoning by Peter M. Schuster,Monika Seisenberger,Andreas Weiermann Pdf

This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students.

Author : Neil Tennant
Publisher : Oxford University Press
Page : 376 pages
File Size : 48,5 Mb
Release : 2022-02-25
Category : Arithmetic
ISBN : 9780192846679

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The Logic of Number by Neil Tennant Pdf

This book develops Tennant's Natural Logicist account of the foundations of the natural, rational, and real numbers. Tennant uses this framework to distinguish the logical from the intuitive aspects of the basic elements of arithmetic.

Author : Fernando Ferreira,Reinhard Kahle,Giovanni Sommaruga
Publisher : Springer Nature
Page : 209 pages
File Size : 44,7 Mb
Release : 2022-10-13
Category : Mathematics
ISBN : 9783030776572

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Axiomatic Thinking I by Fernando Ferreira,Reinhard Kahle,Giovanni Sommaruga Pdf

In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere. The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come. The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations. Chapter 8 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Author : Matthias Schirn
Publisher : Walter de Gruyter
Page : 477 pages
File Size : 51,9 Mb
Release : 2010-12-16
Category : Philosophy
ISBN : 9783110813043

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Importance and Legacy by Matthias Schirn Pdf

Author : Mike Hinchey,Jonathan P. Bowen,Ernst-Rüdiger Olderog
Publisher : Springer
Page : 328 pages
File Size : 51,9 Mb
Release : 2017-03-01
Category : Mathematics
ISBN : 9783319486284

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Provably Correct Systems by Mike Hinchey,Jonathan P. Bowen,Ernst-Rüdiger Olderog Pdf

As computers increasingly control the systems and services we depend upon within our daily lives like transport, communications, and the media, ensuring these systems function correctly is of utmost importance. This book consists of twelve chapters and one historical account that were presented at a workshop in London in 2015, marking the 25th anniversary of the European ESPRIT Basic Research project ‘ProCoS’ (Provably Correct Systems). The ProCoS I and II projects pioneered and accelerated the automation of verification techniques, resulting in a wide range of applications within many trades and sectors such as aerospace, electronics, communications, and retail. The following topics are covered: An historical account of the ProCoS project Hybrid Systems Correctness of Concurrent Algorithms Interfaces and Linking Automatic Verification Run-time Assertions Checking Formal and Semi-Formal Methods Provably Correct Systems provides researchers, designers and engineers with a complete overview of the ProCoS initiative, past and present, and explores current developments and perspectives within the field.

Author : K. Schütte
Publisher : Springer Science & Business Media
Page : 309 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642664731

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Proof Theory by K. Schütte Pdf

This book was originally intended to be the second edition of the book "Beweis theorie" (Grundlehren der mathematischen Wissenschaften, Band 103, Springer 1960), but in fact has been completely rewritten. As well as classical predicate logic we also treat intuitionistic predicate logic. The sentential calculus properties of classical formal and semiformal systems are treated using positive and negative parts of formulas as in the book "Beweistheorie". In a similar way we use right and left parts of formulas for intuitionistic predicate logic. We introduce the theory of functionals of finite types in order to present the Gi:idel interpretation of pure number theory. Instead of ramified type theory, type-free logic and the associated formalization of parts of analysis which we treated in the book "Beweistheorie", we have developed simple classical type theory and predicative analysis in a systematic way. Finally we have given consistency proofs for systems of lI~-analysis following the work of G. Takeuti. In order to do this we have introduced a constni'ctive system of notation for ordinals which goes far beyond the notation system in "Beweistheorie."

Author : Stefano Bloch
Publisher : University of Chicago Press
Page : 212 pages
File Size : 42,9 Mb
Release : 2019-11-14
Category : Biography & Autobiography
ISBN : 9780226493589

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Going All City by Stefano Bloch Pdf

“We could have been called a lot of things: brazen vandals, scared kids, threats to social order, self-obsessed egomaniacs, marginalized youth, outsider artists, trend setters, and thrill seekers. But, to me, we were just regular kids growing up hard in America and making the city our own. Being ‘writers’ gave us something to live for and ‘going all city’ gave us something to strive for; and for some of my friends it was something to die for.” In the age of commissioned wall murals and trendy street art, it’s easy to forget graffiti’s complicated and often violent past in the United States. Though graffiti has become one of the most influential art forms of the twenty-first century, cities across the United States waged a war against it from the late 1970s to the early 2000s, complete with brutal police task forces. Who were the vilified taggers they targeted? Teenagers, usually, from low-income neighborhoods with little to their names except a few spray cans and a desperate need to be seen—to mark their presence on city walls and buildings even as their cities turned a blind eye to them. Going All City is the mesmerizing and painful story of these young graffiti writers, told by one of their own. Prolific LA writer Stefano Bloch came of age in the late 1990s amid constant violence, poverty, and vulnerability. He recounts vicious interactions with police; debating whether to take friends with gunshot wounds to the hospital; coping with his mother’s heroin addiction; instability and homelessness; and his dread that his stepfather would get out of jail and tip his unstable life into full-blown chaos. But he also recalls moments of peace and exhilaration: marking a fresh tag; the thrill of running with his crew at night; exploring the secret landscape of LA; the dream and success of going all city. Bloch holds nothing back in this fierce, poignant memoir. Going All City is an unflinching portrait of a deeply maligned subculture and an unforgettable account of what writing on city walls means to the most vulnerable people living within them.

Author : Sumit K. Mandal
Publisher : Cambridge University Press
Page : 285 pages
File Size : 41,9 Mb
Release : 2018
Category : History
ISBN : 9781107196797

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Becoming Arab by Sumit K. Mandal Pdf

Becoming Arab explores how a long history of inter-Asian interaction fared in the face of nineteenth-century racial categorisation and control.

Author : Annemarie Fritz,Erkan Gürsoy,Moritz Herzog
Publisher : Walter de Gruyter GmbH & Co KG
Page : 432 pages
File Size : 52,5 Mb
Release : 2021-06-08
Category : Language Arts & Disciplines
ISBN : 9783110661941

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Diversity Dimensions in Mathematics and Language Learning by Annemarie Fritz,Erkan Gürsoy,Moritz Herzog Pdf

Wie hängen sprachliche und mathematische Entwicklung zusammen? Dieser Frage wird derzeit mit großem Interesse aus unterschiedlichen Perspektiven nachgegangen. Dieser Sammelband vereint Erkenntnisse aus Psychologie, Neurowissenschaften, Mathematikdidaktik, (Psycho-)Linguistik und Mehrsprachigkeitsforschung. Der interdisziplinäre Ansatz bietet einen umfassenden Blick auf den aktuellen Forschungsstand, dargestellt von national und international renommierten Forschenden. Das Buch gliedert sich in drei Teile. Der erste Teil „Modelle und Theorien“ fasst theoretische Überlegungen zusammen und stellt Strukturen für Forschung und Praxis bereit. Dieser Teil dient dazu, den Grundstein für die anderen Teile sowie für zukünftige Forschung zu legen. Der zweite Teil „Kindergartenalter“ sowie der dritte Teil „Grundschulalter“ decken empirische Befunde über die Korrelation zwischen Sprache und mathematischem Lernen in der jeweiligen Altersgruppe ab. Ein besonderer Fokus liegt hierbei auf dem Aspekt der Mehrsprachigkeit. Damit bietet dieser Sammelband eine große Bandbreite fachspezifischen Wissens für Bildungswissenschaftler*innen, Lehramtsstudierende, Psycholog*innen und Forschende zur Mehrsprachigkeit.