Computability and Complexity in Analysis
Computability and Complexity in Analysis

Author: Jens Blanck

Publisher: Springer

Published: 2003-06-29

Total Pages: 403

ISBN-13: 3540453350

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The workshop on Computability and Complexity in Analysis, CCA 2000, was hosted by the Department of Computer Science of the University of Wales Swansea, September 17{19, 2000. It was the fourth workshop in a successful series of workshops: CCA’95 in Hagen, Germany, CCA’96 in Trier, Germany, and CCA’98 in Brno, Czech Republic. About 40 participants from the countries United Kingdom, Germany, Japan, Italy, Russia, France, Denmark, Greece, and Ireland contributed to the success of this meeting. Altogether, 28 talkswere p- sented in Swansea. These proceedings include 23 papers which represent a cro- section through recent research on computability and complexity in analysis. The workshop succeeded in bringing together people interested in computability and complexity aspects of analysis and in exploring connections with nume- cal methods, physics and, of course, computer science. It was rounded o by a number of talks and papers on exact computer arithmetic and by a competition of v e implemented systems. A report on this competition has been included in these proceedings. We would like to thank the authors for their contributions and the referees for their careful work, and we hope for further inspiring and constructive meetings of the same kind. April 2001 Jens Blanck Vasco Brattka Peter Hertling Organization CCA2000was hosted by the Department of Computer Science of the University of Wales Swansea and took place on September 17{19, 2000.

Model Theory, Algebra, and Geometry
Model Theory, Algebra, and Geometry

Author: Deirdre Haskell

Publisher: Cambridge University Press

Published: 2000-07-03

Total Pages: 244

ISBN-13: 9780521780681

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Model theory has made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. These applications range from a proof of the rationality of certain Poincare series associated to varieties over p-adic fields, to a proof of the Mordell-Lang conjecture for function fields in positive characteristic. In some cases (such as the latter) it is the most abstract aspects of model theory which are relevant. This book, originally published in 2000, arising from a series of introductory lectures for graduate students, provides the necessary background to understanding both the model theory and the mathematics behind these applications. The book is unique in that the whole spectrum of contemporary model theory (stability, simplicity, o-minimality and variations) is covered and diverse areas of geometry (algebraic, diophantine, real analytic, p-adic, and rigid) are introduced and discussed, all by leading experts in their fields.

Professional Practice in Artificial Intelligence
Professional Practice in Artificial Intelligence

Author: John Debenham

Publisher: Springer Science & Business Media

Published: 2006-07-27

Total Pages: 358

ISBN-13: 0387346554

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The Second Symposium on Professional Practice in AI 2006 is a conference within the IFIP World Computer Congress 2006, Santiago, Chile. The Symposium is organised by the IFIP Technical Committee on Artificial Intelligence (Technical Committee 12) and its Working Group 12.5 (Artificial Intelligence Applications). The First Symposium in this series was one of the conferences in the IFIP World Computer Congi-ess 2004, Toulouse France. The conference featured invited talks by Rose Dieng, John Atkinson, John Debenham and Max Bramer. The Symposium was a component of the IFIP AI 2006 conference, organised by Professor Max Bramer. I should like to thank the Symposium General Chair, Professor Bramer for his considerable assistance in making the Symposium happen within a very tight deadline. These proceedings are the result of a considerable amount of hard work. Beginning with the preparation of the submitted papers, the papers were each reviewed by at least two members of the international Program Committee. The authors of accepted papers then revised their manuscripts to produce their final copy. The hard work of the authors, the referees and the Program Committee is gratefully aclaiowledged. The IFIP AI 2006 conference and the Symposium are the latest in a series of conferences organised by IFIP Technical Committee 12 dedicated to the techniques of Aitificial Intelligence and their real-world applications. Further infoirmation about TC12 can be found on our website http;//www.ifiptcI2.org.

CONCUR '96: Concurrency Theory
CONCUR '96: Concurrency Theory

Author: Ugo Montanari

Publisher: Springer Science & Business Media

Published: 1996-08-07

Total Pages: 772

ISBN-13: 9783540616047

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This book constitutes the refereed proceedings of the 8th International Conference on Concurrency Theory, CONCUR'97. held in Warsaw, Poland, in July 1997. The 24 revised full papers presented were selected by the program committee for inclusion in the volume from a total of 41 high-quality submissions. The volume covers all current topics in the science of concurrency theory and its applications, such as reactive systems, hybrid systems, model checking, partial orders, state charts, program logic calculi, infinite state systems, verification, and others.

New Computational Paradigms
New Computational Paradigms

Author: S.B. Cooper

Publisher: Springer Science & Business Media

Published: 2007-11-28

Total Pages: 560

ISBN-13: 0387685464

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This superb exposition of a complex subject examines new developments in the theory and practice of computation from a mathematical perspective, with topics ranging from classical computability to complexity, from biocomputing to quantum computing. This book is suitable for researchers and graduate students in mathematics, philosophy, and computer science with a special interest in logic and foundational issues. Most useful to graduate students are the survey papers on computable analysis and biological computing. Logicians and theoretical physicists will also benefit from this book.

On the extraction of computational content from noneffective convergence proofs in analysis
On the extraction of computational content from noneffective convergence proofs in analysis

Author: Pavol Safarik

Publisher: Logos Verlag Berlin GmbH

Published: 2014

Total Pages: 164

ISBN-13: 3832537651

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The Fields medalist, Terence Tao, recently emphasized the importance of ''hard'' (or finitary) analysis and connected the finitisation to the methods we will employ in this thesis: ... The main advantage of working in a finitary setting ... is that the underlying dynamical system becomes extremely explicit. ... In proof theory, this finitisation is known as Gödel functional interpretation ... For convergence theorems Tao calls the finitary formulation metastability and the corresponding explicit content its rate(s). In the case of the mean ergodic theorem such a rate can be used to obtain even an effective bound on the number of fluctuations. We introduce effective learnability and three other natural kinds of such finitary information and analyze the corresponding proof-theoretic conditions. Effective learnability not only provides means to know when to expect a bound on the number of fluctuations but also explains a very common pattern in the realizers for strong ergodic theorems. Moreover, we will see how a most natural example for a non-learnable convergence theorem closely relates to a notable exception to this pattern, the strong nonlinear ergodic theorem due to Wittmann. Finally, we show how can computational content be extracted in the context of non-standard analysis.

Computability and Models
Computability and Models

Author: Barry S. Cooper

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 388

ISBN-13: 1461507553

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Science involves descriptions of the world we live in. It also depends on nature exhibiting what we can best describe as a high aLgorithmic content. The theme running through this collection of papers is that of the interaction between descriptions, in the form of formal theories, and the algorithmic content of what is described, namely of the modeLs of those theories. This appears most explicitly here in a number of valuable, and substantial, contributions to what has until recently been known as 'recursive model theory' - an area in which researchers from the former Soviet Union (in particular Novosibirsk) have been pre-eminent. There are also articles concerned with the computability of aspects of familiar mathematical structures, and - a return to the sort of basic underlying questions considered by Alan Turing in the early days of the subject - an article giving a new perspective on computability in the real world. And, of course, there are also articles concerned with the classical theory of computability, including the first widely available survey of work on quasi-reducibility. The contributors, all internationally recognised experts in their fields, have been associated with the three-year INTAS-RFBR Research Project "Com putability and Models" (Project No. 972-139), and most have participated in one or more of the various international workshops (in Novosibirsk, Heidelberg and Almaty) and otherresearch activities of the network.

The Proper Treatment of Events
The Proper Treatment of Events

Author: Michiel Van Lambalgen

Publisher: John Wiley & Sons

Published: 2008-04-15

Total Pages: 266

ISBN-13: 0470759224

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The Proper Treatment of Events offers a novel approach to the semantics of tense and aspect motivated by cognitive considerations. offers a new theory of the semantics of tense aspect and nominalizations that combines formal semantics and cognitive approaches written accessibly for students and scholars in theoretical linguists, as well as in philosophy of language, logic, cognitive science, and computer science accompanied by a website at (http://staff.science.uva.nl/~michiell/) that provides slides for instructors and background material for students

Reflections on the Foundations of Mathematics
Reflections on the Foundations of Mathematics

Author: Wilfried Sieg

Publisher: Cambridge University Press

Published: 2017-03-30

Total Pages: 456

ISBN-13: 1316998819

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Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the fifteenth publication in the Lecture Notes in Logic series, collects papers presented at the symposium 'Reflections on the Foundations of Mathematics' held in celebration of Solomon Feferman's 70th birthday (The 'Feferfest') at Stanford University, California in 1988. Feferman has shaped the field of foundational research for nearly half a century. These papers reflect his broad interests as well as his approach to foundational research, which emphasizes the solution of mathematical and philosophical problems. There are four sections, covering proof theoretic analysis, logic and computation, applicative and self-applicative theories, and philosophy of modern mathematical and logic thought.

Dynamic Formal Epistemology
Dynamic Formal Epistemology

Author: Patrick Girard

Publisher: Springer Science & Business Media

Published: 2011-01-06

Total Pages: 247

ISBN-13: 9400700741

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This volume is a collation of original contributions from the key actors of a new trend in the contemporary theory of knowledge and belief, that we call “dynamic epistemology”. It brings the works of these researchers under a single umbrella by highlighting the coherence of their current themes, and by establishing connections between topics that, up until now, have been investigated independently. It also illustrates how the new analytical toolbox unveils questions about the theory of knowledge, belief, preference, action, and rationality, in a number of central axes in dynamic epistemology: temporal, social, probabilistic and even deontic dynamics.