Proof And Computation II: From Proof Theory And Univalent Mathematics To Program Extraction And Verification - Hardcover

Klaus Mainzer; Peter Schuster; Helmut Schwichtenberg

Hardcover

ISBN 10: 981123647X ISBN 13: 9789811236471

Publisher: World Scientific Publishing, 2021

Synopsis

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.

About this title

About the Author

Klaus Mainzer is Emeritus of Excellence at the Technical University of Munich (TUM). After studies of mathematics, physics, and philosophy at the University of Münster, he was professor for the foundations and history of exact sciences and vice-president at the University of Constance, professor for philosophy of science and director of the institute of interdisciplinary informatics at the University of Augsburg, and professor for philosophy of science, director of the Carl von Linde Academy and founding director of the Munich Center for Technology in Society (MCTS) at TUM. His principal research interests are about constructive and computational foundations of mathematics, science, and philosophy with a special focus on AItechnology and its societal impact.

 

Peter Schuster is Professor for Mathematical Logic at the University of Verona. After both doctorate and habilitation in mathematics he was Privatdozent at the University of Munich, and Lecturer at the University of Leeds. Apart from constructive mathematics at large, his principal research interests are about Hilbert's programme in abstract mathematics, especially the computational content of classical proofs in algebra and related fields in which transfinite methods such as Zorn's Lemma are invoked.

 

Helmut Schwichtenberg is an Emeritus Professor of Mathematics at Ludwig-Maximilians-Universität München. After both doctorate and habilitation at the Institut für Mathematische Logik der Fakultät für Mathematik, Universität Münster he was Wissenschaftlicher Rat und Professor at Universität Heidelberg, before becoming Professor (Ordinarius) at Ludwig-Maximilians-Universität München. His principal research interests are proof theory, lambda calculus, recursion theory, and applications of logic to computer science.

Edition details

• Publisher: World Scientific Publishing
• Publication date: 2021
• ISBN 10: 981123647X
• ISBN 13: 9789811236471
• Binding: Hardcover
• Language: English
• Number of pages: 424