Aspects of Incompleteness

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Author: Per Lindström

Publisher: Cambridge University Press

ISBN: 1107167922

Category: Mathematics

Page: 142

View: 9729

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. In this volume, the tenth publication in the Lecture Notes in Logic series, Per Lindström presents some of the main topics and results in general metamathematics. In addition to standard results of Gödel et al. on incompleteness, (non-)finite axiomatizability, and interpretability, this book contains a thorough treatment of partial conservativity and degrees of interpretability. It comes complete with exercises, and will be useful as a textbook for graduate students with a background in logic, as well as a valuable resource for researchers.

Logic in Tehran

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Author: Ali Enayat,Iraj Kalantari,Mojtaba Moniri

Publisher: Cambridge University Press

ISBN: 1108670008

Category: Mathematics

Page: N.A

View: 6259

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 twenty-sixth publication in the Lecture Notes in Logic series, contains the proceedings of the 'Workshop and Conference on Logic, Algebra and Arithmetic' held at the Institute for Studies in Theoretical Physics and Mathematics (IPM) in Tehran, Iran in October, 2003. These papers are mostly revised and expanded versions of those that were originally presented at the meeting and address all areas of mathematical logic. The book also includes a short history of mathematical logic in Iran.

Handbook of Proof Theory

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Author: S.R. Buss

Publisher: Elsevier

ISBN: 9780080533186

Category: Mathematics

Page: 810

View: 9516

This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.

Aspects of Philosophical Logic

Some Logical Forays into Central Notions of Linguistics and Philosophy

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Author: Uwe Mönnich

Publisher: Springer Science & Business Media

ISBN: 9400983840

Category: Philosophy

Page: 290

View: 6548

This volume constitutes the Proceedings of a workshop on formal seman tics of natural languages which was held in Tiibingen from the 1st to the 3rd of December 1977. Its main body consists of revised versions of most of the papers presented on that occasion. Three supplementary papers (those by Gabbay and Sma by) are included because they seem to be of particular interest in their respective fields. The area covered by the work of scholars engaged in philosophical logic and the formal analysis of natural languages testifies to the live liness in those disciplines. It would have been impossible to aim at a complete documentation of relevant research within the limits imposed by a short conference whereas concentration on a single topic would have conveyed the false impression of uniformity foreign to a young and active field. It is hoped that the essays collected in this volume strike a reasonable balance between the two extremes. The topics discussed here certainly belong to the most important ones enjoying the attention of linguists and philosophers alike: the analysis of tense in formal and natural languages (van Benthem, Gabbay), the quickly expanding domain of generalized quantifiers (Goldblatt), the problem of vagueness (Kamp), the connected areas of pronominal reference (Smaby) and presupposition (von Stechow) and, last but not least, modal logic as a sort of all-embracing theoretical framework (Bressan). The workshop which led to this collection formed part of the activities celebrating the 500th anniversary of Tiibingen University.

The Logic of Provability

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Author: George Boolos

Publisher: Cambridge University Press

ISBN: 9780521483254

Category: Philosophy

Page: 275

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Boolos, a pre-eminent philosopher of mathematics, investigates the relationship between provability and modal logic.

Philosophy of Mathematics

5 Questions

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Author: Vincent F. Hendricks,Hannes Leitgeb

Publisher: Automatic Press Publishing

ISBN: 9788799101351

Category: Mathematics

Page: 342

View: 7611

Philosophy of Mathematics: 5 Questions is a collection of short interviews based on 5 questions presented to some of the most influential and prominent scholars in this field. We hear their views aim, scope, use, the future direction and how their work fits in these respects.

Kurt Gödel: Collected Works:

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Author: Kurt Gödel

Publisher: Clarendon Press

ISBN: 0191003778

Category: Mathematics

Page: 692

View: 3624

Kurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Gödel's publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass. These long-awaited final two volumes contain Gödel's correspondence of logical, philosophical, and scientific interest. Volume IV covers A to G, with H to Z in volume V; in addition, Volume V contains a full inventory of Gödel's Nachlass. All volumes include introductory notes that provide extensive explanatory and historical commentary on each body of work, English translations of material originally written in German (some transcribed from the Gabelsberger shorthand), and a complete bibliography of all works cited. Kurt Gödel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy. The only comprehensive edition of Gödel's work available, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science and all others who wish to be acquainted with one of the great minds of the twentieth century.

Correspondence H-Z

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Author: Kurt Gödel,S. Feferman

Publisher: Oxford University Press

ISBN: 9780198500759

Category: Computers

Page: 690

View: 454

Kurt Gödel (1906 - 1978) was the most outstanding logician of the twentieth century, famous for his hallmark works on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum hypothesis. He is also noted for his work on constructivity, the decision problem, and the foundations of computability theory, as well as for the strong individuality of his writings on the philosophy of mathematics. He is less well known for his discovery of unusual cosmological models for Einstein's equations, in theory permitting time travel into the past. The Collected Works is a landmark resource that draws together a lifetime of creative thought and accomplishment. The first two volumes were devoted to Gödel's publications in full (both in original and translation), and the third volume featured a wide selection of unpublished articles and lecture texts found in Gödel's Nachlass. These long-awaited final two volumes contain Gödel's correspondence of logical, philosophical, and scientific interest. Volume IV covers A to G, with H to Z in volume V; in addition, Volume V contains a full inventory of Gödel's Nachlass. L All volumes include introductory notes that provide extensive explanatory and historical commentary on each body of work, English translations of material originally written in German (some transcribed from the Gabelsberger shorthand), and a complete bibliography of all works cited. Kurt Gödel: Collected Works is designed to be useful and accessible to as wide an audience as possible without sacrificing scientific or historical accuracy. The only comprehensive edition of Gödel's work available, it will be an essential part of the working library of professionals and students in logic, mathematics, philosophy, history of science, and computer science and all others who wish to be acquainted with one of the great minds of the twentieth century.

Goedel's Way

Exploits into an undecidable world

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Author: Gregory Chaitin,Francisco A Doria,Newton C.A. da Costa

Publisher: CRC Press

ISBN: 0415690854

Category: Mathematics

Page: 160

View: 3254

Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various areas, ranging from chaos theory and physics to economics and even ecology. In this lively treatise, based on Chaitin’s groundbreaking work and on the da Costa-Doria results in physics, ecology, economics and computer science, the authors show that the Gödel incompleteness phenomenon can directly bear on the practice of science and perhaps on our everyday life. This accessible book gives a new, detailed and elementary explanation of the Gödel incompleteness theorems and presents the Chaitin results and their relation to the da Costa-Doria results, which are given in full, but with no technicalities. Besides theory, the historical report and personal stories about the main character and on this book’s writing process, make it appealing leisure reading for those interested in mathematics, logic, physics, philosophy and computer sciences. See also: http://www.youtube.com/watch?v=REy9noY5Sg8

Kurt Gödel

Essays for his Centennial

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Author: Solomon Feferman,Charles Parsons,Stephen G. Simpson

Publisher: Cambridge University Press

ISBN: 1139487752

Category: Mathematics

Page: N.A

View: 6730

Kurt Gödel (1906–1978) did groundbreaking work that transformed logic and other important aspects of our understanding of mathematics, especially his proof of the incompleteness of formalized arithmetic. This book on different aspects of his work and on subjects in which his ideas have contemporary resonance includes papers from a May 2006 symposium celebrating Gödel's centennial as well as papers from a 2004 symposium. Proof theory, set theory, philosophy of mathematics, and the editing of Gödel's writings are among the topics covered. Several chapters discuss his intellectual development and his relation to predecessors and contemporaries such as Hilbert, Carnap, and Herbrand. Others consider his views on justification in set theory in light of more recent work and contemporary echoes of his incompleteness theorems and the concept of constructible sets.

Logic Colloquium 2006

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Author: S. Barry Cooper

Publisher: Cambridge University Press

ISBN: 0521110815

Category: Mathematics

Page: 373

View: 9743

The 2006 proceedings from the Annual European Meeting of the Association for Symbolic Logic, also known as the Logic Colloquium.

Logic Colloquium '03

Lecture Notes in Logic 24

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Author: Viggo Stoltenberg-Hansen,Jouko Väänänen

Publisher: A K Peters/CRC Press

ISBN: N.A

Category: Mathematics

Page: 408

View: 2479

This book is a compilation of papers resented at the 2003 European Summer Meeting of the Association for Symbolic Logic. It includes tutorials and research articles from some of the world's preeminent logicians. Of particular interest is a tutorial on finite model theory and query languages that lie between first-order and second-order logic. Other articles cover current research topics in all areas of mathematical logic, including Proof Theory, Set Theory, Model Theory, Computability Theory, and Philosophy.

Perception-Based Data Processing in Acoustics

Applications to Music Information Retrieval and Psychophysiology of Hearing

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Author: Bozena Kostek

Publisher: Springer Science & Business Media

ISBN: 9783540257295

Category: Computers

Page: 420

View: 1396

This monograph provides novel insights into cognitive mechanisms underlying the processing of sound and music in different environments. A solid understanding of these mechanisms is vital for numerous technological applications such as for example information retrieval from distributed musical databases or building expert systems. In order to investigate the cognitive mechanisms of music perception fundamentals of hearing psychophysiology and principles of music perception are presented. In addition, some computational intelligence methods are reviewed, such as rough sets, fuzzy logic, artificial neural networks, decision trees and genetic algorithms. The applications of hybrid decision systems to problem solving in music and acoustics are exemplified and discussed on the basis of obtained experimental results.

Proceedings of the International Congress of Mathematicians

Madrid, August 22-30, 2006

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Author: Marta Sanz Solé

Publisher: Amer Mathematical Society

ISBN: 9783037190227

Category: Mathematics

Page: 4500

View: 7682

The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress. The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject. Information for our distributors: Distributed within the Americas by the American Mathematical Society. All commerical channel discounts apply.

Advances in Computing and Information - ICCI '90

International Conference on Computing and Information Niagara Falls, Canada, May 23-26, 1990. Proceedings

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Author: Selim G. Akl,F. Fiala,Waldemar W. Koczkodaj

Publisher: Springer Science & Business Media

ISBN: 9783540535041

Category: Computers

Page: 529

View: 9032

This volume contains selected and invited papers presented at ICCI '90. Topics range over theory of comput- ing, algorithms and programming, data and software engineering, computer architecture, concurrency, parallelism, communication and networking.

An Introduction to Mathematical Logic and Type Theory

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Author: Peter B. Andrews

Publisher: Springer Science & Business Media

ISBN: 9781402007637

Category: Computers

Page: 390

View: 3529

In case you are considering to adopt this book for courses with over 50 students, please contact [email protected] for more information. This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.