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Thirty Five Years Of Automating Mathematics

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Thirty Five Years Of Automating Mathematics

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Author : F.D. Kamareddine
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Thirty Five Years Of Automating Mathematics written by F.D. Kamareddine 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 2013-04-17 with Mathematics categories.

THIRTY FIVE YEARS OF AUTOMATING MATHEMATICS: DEDICATED TO 35 YEARS OF DE BRUIJN'S AUTOMATH N. G. de Bruijn was a well established mathematician before deciding in 1967 at the age of 49 to work on a new direction related to Automating Mathematics. By then, his contributions in mathematics were numerous and extremely influential. His book on advanced asymptotic methods, North Holland 1958, was a classic and was subsequently turned into a book in the well known Dover book series. His work on combinatorics yielded influential notions and theorems of which we mention the de Bruijn-sequences of 1946 and the de Bruijn-Erdos theorem of 1948. De Bruijn's contributions to mathematics also included his work on generalized function theory, analytic number theory, optimal control, quasicrystals, the mathematical analysis of games and much more. In the 1960s de Bruijn became fascinated by the new computer technology and as a result, decided to start the new AUTOMATH project where he could check, with the help of the computer, the correctness of books of mathematics. In each area that de Bruijn approached, he shed a new light and was known for his originality and for making deep intellectual contributions. And when it came to automating mathematics, he again did it his way and introduced the highly influential AUTOMATH. In the past decade he has also been working on theories of the human brain.

Thirty Five Years Of Automating Mathematics

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Author : F. D. Kamareddine
language : en
Publisher:
Release Date : 2014-01-15

Thirty Five Years Of Automating Mathematics written by F. D. Kamareddine and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Mathematical Knowledge Management

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Author : Andrea Asperti
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-09-07

Mathematical Knowledge Management written by Andrea Asperti 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 2004-09-07 with Computers categories.

This book constitutes the refereed proceedings of the Third International Conference on Mathematical Knowledge Management, MKM 2004, held in Bialowieza, Poland, in September 2004. The 27 revised full papers presented were carefully reviewed and selected from 48 submissions. Among the topics addressed are mathematics retrieval, formalizing mathematics, formal mathematics, digital mathematical libraries, semantic Web, knowledge repositories, mathematical knowledge representation, theorem proving systems, OWL, proof verification, formal representation, mathematical formulae processing, and the OpenMath project.

Automated Deduction Cade 28

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Author : André Platzer
language : en
Publisher: Springer Nature
Release Date : 2021-07-07

Automated Deduction Cade 28 written by André Platzer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-07 with Computers categories.

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.

Thirty Five Years Of Automating Mathematics

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Author : F.D. Kamareddine
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-11-30

Finitely Supported Mathematics

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Author : Andrei Alexandru
language : en
Publisher: Springer
Release Date : 2016-08-01

Finitely Supported Mathematics written by Andrei Alexandru and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-01 with Computers categories.

In this book the authors present an alternative set theory dealing with a more relaxed notion of infiniteness, called finitely supported mathematics (FSM). It has strong connections to the Fraenkel-Mostowski (FM) permutative model of Zermelo-Fraenkel (ZF) set theory with atoms and to the theory of (generalized) nominal sets. More exactly, FSM is ZF mathematics rephrased in terms of finitely supported structures, where the set of atoms is infinite (not necessarily countable as for nominal sets). In FSM, 'sets' are replaced either by `invariant sets' (sets endowed with some group actions satisfying a finite support requirement) or by `finitely supported sets' (finitely supported elements in the powerset of an invariant set). It is a theory of `invariant algebraic structures' in which infinite algebraic structures are characterized by using their finite supports. After explaining the motivation for using invariant sets in the experimental sciences as well as the connections with the nominal approach, admissible sets and Gandy machines (Chapter 1), the authors present in Chapter 2 the basics of invariant sets and show that the principles of constructing FSM have historical roots both in the definition of Tarski `logical notions' and in the Erlangen Program of Klein for the classification of various geometries according to invariants under suitable groups of transformations. Furthermore, the consistency of various choice principles is analyzed in FSM. Chapter 3 examines whether it is possible to obtain valid results by replacing the notion of infinite sets with the notion of invariant sets in the classical ZF results. The authors present techniques for reformulating ZF properties of algebraic structures in FSM. In Chapter 4 they generalize FM set theory by providing a new set of axioms inspired by the theory of amorphous sets, and so defining the extended Fraenkel-Mostowski (EFM) set theory. In Chapter 5 they define FSM semantics for certain process calculi (e.g., fusion calculus), and emphasize the links to the nominal techniques used in computer science. They demonstrate a complete equivalence between the new FSM semantics (defined by using binding operators instead of side conditions for presenting the transition rules) and the known semantics of these process calculi. The book is useful for researchers and graduate students in computer science and mathematics, particularly those engaged with logic and set theory.

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.

Mathematics Computer Science And Logic A Never Ending Story

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Author : Peter Paule
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-17

Mathematics Computer Science And Logic A Never Ending Story written by Peter Paule 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 2013-09-17 with Computers categories.

This book presents four mathematical essays which explore the foundations of mathematics and related topics ranging from philosophy and logic to modern computer mathematics. While connected to the historical evolution of these concepts, the essays place strong emphasis on developments still to come. The book originated in a 2002 symposium celebrating the work of Bruno Buchberger, Professor of Computer Mathematics at Johannes Kepler University, Linz, Austria, on the occasion of his 60th birthday. Among many other accomplishments, Professor Buchberger in 1985 was the founding editor of the Journal of Symbolic Computation; the founder of the Research Institute for Symbolic Computation (RISC) and its chairman from 1987-2000; the founder in 1990 of the Softwarepark Hagenberg, Austria, and since then its director. More than a decade in the making, Mathematics, Computer Science and Logic - A Never Ending Story includes essays by leading authorities, on such topics as mathematical foundations from the perspective of computer verification; a symbolic-computational philosophy and methodology for mathematics; the role of logic and algebra in software engineering; and new directions in the foundations of mathematics. These inspiring essays invite general, mathematically interested readers to share state-of-the-art ideas which advance the never ending story of mathematics, computer science and logic. Mathematics, Computer Science and Logic - A Never Ending Story is edited by Professor Peter Paule, Bruno Buchberger’s successor as director of the Research Institute for Symbolic Computation.

Intelligent Computer Mathematics

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Author : Jacques Carette
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-06

Intelligent Computer Mathematics written by Jacques Carette 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 2009-07-06 with Computers categories.

As computers and communications technology advance, greater opportunities arise for intelligent mathematical computation. While computer algebra, au- mated deduction and mathematical publishing each have long and successful histories, we are now seeing increasing opportunities for synergy among them. The Conferences on Intelligent Computer Mathematics (cicm 2009) is a c- lection of co-located meetings, allowing researchers and practitioners active in these related areas to share recent results and identify the next challenges. The speci?c areas of the cicm conferences and workshops are described below, but the unifying theme is the computerized handling of mathematical knowledge. The successful formalization of much of mathematics, as well as a better - derstanding of its internal structure, makes mathematical knowledge in many waysmore tractable than generalknowledge,as traditionally treatedin arti?cial intelligence. Similarly, we can also expect the problem of e?ectively using ma- ematical knowledge in automated ways to be much more tractable. This is the goal of the work in the cicm conferences and workshops. In the long view, so- ing the problems addressed by cicm is an important milestone in formulating the next generation of mathematical software.

Fields Of Logic And Computation Iii

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Author : Andreas Blass
language : en
Publisher: Springer Nature
Release Date : 2020-05-22

Fields Of Logic And Computation Iii written by Andreas Blass and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-22 with Computers categories.

This Festschrift is published in honor of Yuri Gurevich’s 80th birthday. An associated conference, YuriFest 2020, was planned for May 18–20 in Fontainebleau, France, in combination with the 39th Journées sur les Arithmétiques Faibles also celebrating Yuri’s 80th birthday. Because of the coronavirus situation, the conference had to be postponed, but this Festschrift is being published as originally planned. It addresses a very wide variety of topics, but by no means all of the fields of logic and computation in which Yuri has made important progress.

Thirty Five Years Of Automating Mathematics

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