From Sets and Types to Topology and Analysis

Towards Practicable Foundations for Constructive Mathematics

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Author: Laura Crosilla,Peter Schuster

Publisher: Oxford University Press on Demand

ISBN: 0198566514

Category: Mathematics

Page: 350

View: 3507

Bridging the foundations and practice of constructive mathematics, this text focusses on the contrast between the theoretical developments - which have been most useful for computer science - and more specific efforts on constructive analysis, algebra and topology.

Computer Science Logic

23rd International Workshop, CSL 2009, 18th Annual Conference of the EACSL, Coimbra, Portugal, September 7-11, 2009, Proceedings

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Author: Erich Grädel,Reinhard Kahle

Publisher: Springer Science & Business Media

ISBN: 3642040268

Category: Computers

Page: 567

View: 4555

This book constitutes the proceedings of the 23rd International Workshop on Computer Science Logic, CSL 2009, held in Coimbra, Portugal, in September 2009. The 34 papers presented together with 5 invited talks were carefully reviewed and selected from 89 full paper submissions. All current aspects of logic in computer science are addressed, ranging from foundational and methodological issues to application issues of practical relevance. The book concludes with a presentation of this year's Ackermann award, the EACSL Outstanding Dissertation Award for Logic in Computer Science.

Logic, Mathematics, Philosophy, Vintage Enthusiasms

Essays in Honour of John L. Bell

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Author: David DeVidi,Michael Hallett,Peter Clark

Publisher: Springer Science & Business Media

ISBN: 9789400702141

Category: Philosophy

Page: 486

View: 1389

The volume includes twenty-five research papers presented as gifts to John L. Bell to celebrate his 60th birthday by colleagues, former students, friends and admirers. Like Bell’s own work, the contributions cross boundaries into several inter-related fields. The contributions are new work by highly respected figures, several of whom are among the key figures in their fields. Some examples: in foundations of maths and logic (William Lawvere, Peter Aczel, Graham Priest, Giovanni Sambin); analytical philosophy (Michael Dummett, William Demopoulos), philosophy of science (Michael Redhead, Frank Arntzenius), philosophy of mathematics (Michael Hallett, John Mayberry, Daniel Isaacson) and decision theory and foundations of economics (Ken Bimore). Most articles are contributions to current philosophical debates, but contributions also include some new mathematical results, important historical surveys, and a translation by Wilfrid Hodges of a key work of arabic logic.

Logicism, Intuitionism, and Formalism

What Has Become of Them?

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Author: Sten Lindström,Erik Palmgren,Krister Segerberg,Viggo Stoltenberg-Hansen

Publisher: Springer Science & Business Media

ISBN: 1402089260

Category: Mathematics

Page: 512

View: 971

This anthology reviews the programmes in the foundations of mathematics from the classical period and assesses their possible relevance for contemporary philosophy of mathematics. A special section is concerned with constructive mathematics.

Simplicity Theory

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Author: Byunghan Kim

Publisher: OUP Oxford

ISBN: 0191511587

Category: Mathematics

Page: 272

View: 5810

Model theory, a major branch of mathematical logic, plays a key role connecting logic and other areas of mathematics such as algebra, geometry, analysis, and combinatorics. Simplicity theory, a subject of model theory, studies a class of mathematical structures, called simple. The class includes all stable structures (vector spaces, modules, algebraically closed fields, differentially closed fields, and so on), and also important unstable structures such as the random graph, smoothly approximated structures, pseudo-finite fields, ACFA and more. Simplicity theory supplies the uniform model theoretic points of views to such structures in addition to their own mathematical analyses. This book starts with an introduction to the fundamental notions of dividing and forking, and covers up to the hyperdefinable group configuration theorem for simple theories. It collects up-to-date knowledge on simplicity theory and it will be useful to logicians, mathematicians and graduate students working on model theory.

Foundations of Constructive Mathematics

Metamathematical Studies

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Author: M.J. Beeson

Publisher: Springer Science & Business Media

ISBN: 3642689523

Category: Mathematics

Page: 466

View: 3082

This book is about some recent work in a subject usually considered part of "logic" and the" foundations of mathematics", but also having close connec tions with philosophy and computer science. Namely, the creation and study of "formal systems for constructive mathematics". The general organization of the book is described in the" User's Manual" which follows this introduction, and the contents of the book are described in more detail in the introductions to Part One, Part Two, Part Three, and Part Four. This introduction has a different purpose; it is intended to provide the reader with a general view of the subject. This requires, to begin with, an elucidation of both the concepts mentioned in the phrase, "formal systems for constructive mathematics". "Con structive mathematics" refers to mathematics in which, when you prove that l a thing exists (having certain desired properties) you show how to find it. Proof by contradiction is the most common way of proving something exists without showing how to find it - one assumes that nothing exists with the desired properties, and derives a contradiction. It was only in the last two decades of the nineteenth century that mathematicians began to exploit this method of proof in ways that nobody had previously done; that was partly made possible by the creation and development of set theory by Georg Cantor and Richard Dedekind.

Foundations of Constructive Analysis

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Author: Errett Bishop

Publisher: Ishi Press

ISBN: 9784871877145

Category: Mathematics

Page: 404

View: 1441

This book, Foundations of Constructive Analysis, founded the field of constructive analysis because it proved most of the important theorems in real analysis by constructive methods. The author, Errett Albert Bishop, born July 10, 1928, was an American mathematician known for his work on analysis. In the later part of his life Bishop was seen as the leading mathematician in the area of Constructive mathematics. From 1965 until his death, he was professor at the University of California at San Diego.

Constructive Analysis

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Author: E. Bishop,Douglas S. Bridges

Publisher: Springer Science & Business Media

ISBN: 3642616674

Category: Mathematics

Page: 477

View: 989

This work grew out of Errett Bishop's fundamental treatise 'Founda tions of Constructive Analysis' (FCA), which appeared in 1967 and which contained the bountiful harvest of a remarkably short period of research by its author. Truly, FCA was an exceptional book, not only because of the quantity of original material it contained, but also as a demonstration of the practicability of a program which most ma thematicians believed impossible to carry out. Errett's book went out of print shortly after its publication, and no second edition was produced by its publishers. Some years later, 'by a set of curious chances', it was agreed that a new edition of FCA would be published by Springer Verlag, the revision being carried out by me under Errett's supervision; at the same time, Errett gener ously insisted that I become a joint author. The revision turned out to be much more substantial than we had anticipated, and took longer than we would have wished. Indeed, tragically, Errett died before the work was completed. The present book is the result of our efforts. Although substantially based on FCA, it contains so much new material, and such full revision and expansion of the old, that it is essentially a new book. For this reason, and also to preserve the integrity of the original, I decided to give our joint work a title of its own. Most of the new material outside Chapter 5 originated with Errett.

Constructing Architecture

Materials, Processes, Structures

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Author: Andrea Deplazes

Publisher: Springer Science & Business Media

ISBN: 3764371900

Category: Architecture

Page: 508

View: 7387

Now in its second edition: the trailblazing introduction and textbook on construction includes a new section on translucent materials and an article on the use of glass.

The Resolution of Singular Algebraic Varieties

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Author: David Ellwood,Herwig Hauser,Shigefumi Mori,Josef Schicho

Publisher: American Mathematical Soc.

ISBN: 0821889826

Category: Mathematics

Page: 340

View: 3866

Resolution of Singularities has long been considered as being a difficult to access area of mathematics. The more systematic and simpler proofs that have appeared in the last few years in zero characteristic now give us a much better understanding of singularities. They reveal the aesthetics of both the logical structure of the proof and the various methods used in it. The present volume is intended for readers who are not yet experts but always wondered about the intricacies of resolution. As such, it provides a gentle and quite comprehensive introduction to this amazing field. The book may tempt the reader to enter more deeply into a topic where many mysteries--especially the positive characteristic case--await to be disclosed. Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).

On Fuzziness

A Homage to Lotfi A. Zadeh –

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Author: Rudolf Seising,Enric Trillas,Claudio Moraga,Settimo Termini

Publisher: Springer

ISBN: 3642356419

Category: Computers

Page: 431

View: 5552

The notion of Fuzziness stands as one of the really new concepts that have recently enriched the world of Science. Science grows not only through technical and formal advances on one side and useful applications on the other side, but also as consequence of the introduction and assimilation of new concepts in its corpus. These, in turn, produce new developments and applications. And this is what Fuzziness, one of the few new concepts arisen in the XX Century, has been doing so far. This book aims at paying homage to Professor Lotfi A. Zadeh, the “father of fuzzy logic” and also at giving credit to his exceptional work and personality. In a way, this is reflected in the variety of contributions collected in the book. In some of them the authors chose to speak of personal meetings with Lotfi; in others, they discussed how certain papers of Zadeh were able to open for them a new research horizon. Some contributions documented results obtained from the author/s after taking inspiration from a particular idea of Zadeh, thus implicitly acknowledging him. Finally, there are contributions of several “third generation fuzzysists or softies” who were firstly led into the world of Fuzziness by a disciple of Lotfi Zadeh, who, following his example, took care of opening for them a new road in science. Rudolf Seising is Adjoint Researcher at the European Centre for Soft Computing in Mieres, Asturias (Spain). Enric Trillas and Claudio Moraga are Emeritus Researchers at the European Centre for Soft Computing, Mieres, Asturias (Spain). Settimo Termini is Professor of Theoretical Computer Science at the University of Palermo, Italy and Affiliated Researcher at the European Centre for Soft Computing, Mieres, Asturias (Spain)

Computational Science and Its Applications -- ICCSA 2013

13th International Conference, ICCSA 2013, Ho Chi Minh City, Vietnam, June 24-27, 2013, Proceedings

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Author: Beniamino Murgante,Sanjay Misra,Maurizio Carlini,Carmelo Maria Torre,Hong-Quang Nguyen,David Taniar,Bernady O. Apduhan,Osvaldo Gervasi

Publisher: Springer

ISBN: 3642396402

Category: Computers

Page: 659

View: 4043

The five-volume set LNCS 7971-7975 constitutes the refereed proceedings of the 13th International Conference on Computational Science and Its Applications, ICCSA 2013, held in Ho Chi Minh City, Vietnam in June 2013. The 248 revised papers presented in five tracks and 33 special sessions and workshops were carefully reviewed and selected. The 46 papers included in the five general tracks are organized in the following topical sections: computational methods, algorithms and scientific applications; high-performance computing and networks; geometric modeling, graphics and visualization; advanced and emerging applications; and information systems and technologies. The 202 papers presented in special sessions and workshops cover a wide range of topics in computational sciences ranging from computational science technologies to specific areas of computational sciences such as computer graphics and virtual reality.

The Logic of Scientific Discovery

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Author: Karl Popper

Publisher: Routledge

ISBN: 1134470029

Category: Philosophy

Page: 480

View: 8215

Described by the philosopher A.J. Ayer as a work of 'great originality and power', this book revolutionized contemporary thinking on science and knowledge. Ideas such as the now legendary doctrine of 'falsificationism' electrified the scientific community, influencing even working scientists, as well as post-war philosophy. This astonishing work ranks alongside The Open Society and Its Enemies as one of Popper's most enduring books and contains insights and arguments that demand to be read to this day.

Logical Approaches to Computational Barriers

Second Conference on Computability in Europe, CiE 2006, Swansea, UK, June 30-July 5, 2006, Proceedings

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Author: Arnold Beckmann,Ulrich Berger,Benedikt Löwe,John V. Tucker

Publisher: Springer

ISBN: 3540354689

Category: Computers

Page: 608

View: 5296

This book constitutes the refereed proceedings of the Second International Conference on Computability in Europe, CiE 2006, held in Swansea, UK, June/July 2006. The book presents 31 revised full papers together with 30 invited papers, including papers corresponding to 8 plenary talks and 6 special sessions on proofs and computation, computable analysis, challenges in complexity, foundations of programming, mathematical models of computers and hypercomputers, and Gödel centenary: Gödel's legacy for computability.

State, Space, World

Selected Essays

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Author: Henri Lefebvre

Publisher: U of Minnesota Press

ISBN: 081665316X

Category: Political Science

Page: 330

View: 3653

Making the political aspect of Lefebvre's work available in English for the first time, this book contains essays on philosophy, political theory, state formation, spatial planning, and globalization, as well as provocative reflections on the possibilities and limits of grassroots democracy under advanced capitalism.