Selected Papers in Proof Theory
Author | : G. E. Mint͡s |
Publisher | : |
Total Pages | : 304 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : |
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Author | : G. E. Mint͡s |
Publisher | : |
Total Pages | : 304 |
Release | : 1992 |
Genre | : Mathematics |
ISBN | : |
Author | : Grigorii E. Mints |
Publisher | : North-Holland |
Total Pages | : 294 |
Release | : 1992-01-01 |
Genre | : |
ISBN | : 9780444896193 |
This collection includes papers devoted to the structural theory of proofs, which was born in the framework of Hilbert's program and is applied now in connection with various projects using the effective contents of formalized proofs. The main tool and unifying topic here is normalization, i.e. putting proofs into a normal form. The book presupposes some familiarity with the definition and elementary properties of Gentzen-type systems but little more. The first three papers introduce various normalization procedures different from popular ones. The next group deals with unwinding proofs, that is the extraction of an explicit realization from the proof of existential theorems. Normalization (or more precisely, normal form theorems) is applied to the solution of some problems in the following two papers. A separate group is formed by three papers dealing with applications of the theory of proofs to algebra, more specifically to coherence theorems in category theory. The last paper of the volume is a survey of proof theory and elementary model theory for modal logic up to the year 1974.
Author | : Thorsten Altenkirch |
Publisher | : Springer |
Total Pages | : 222 |
Release | : 2003-06-29 |
Genre | : Computers |
ISBN | : 3540481672 |
This book constitutes the strictly refereed post-workshop proceedings of the International Workshop on Types for Proofs and Programs, TYPES '98, held under the auspices of the ESPRIT Working Group 21900. The 14 revised full papers presented went through a thorough process of reviewing and revision and were selected from a total of 25 candidate papers. All current aspects of type theory and type systems and their relation to proof theory are addressed.
Author | : Calvin C. Elgot |
Publisher | : Springer Science & Business Media |
Total Pages | : 475 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461381770 |
Cal Elgot was a very serious and thoughtful researcher, who with great determi nation attempted to find basic explanations for certain mathematical phenomena as the selection of papers in this volume well illustrate. His approach was, for the most part, rather finitist and constructivist, and he was inevitably drawn to studies of the process of computation. It seems to me that his early work on decision problems relating automata and logic, starting with his thesis under Roger Lyndon and continuing with joint work with Biichi, Wright, Copi, Rutledge, Mezei, and then later with Rabin, set the stage for his attack on the theory of computation through the abstract treatment of the notion of a machine. This is also apparent in his joint work with A. Robinson reproduced here and in his joint papers with John Shepherdson. Of course in the light of subsequent work on decision problems by Biichi, Rabin, Shelah, and many, many others, the subject has been placed on a completely different plane from what it was when Elgot left the area. But I feel that his papers, results-and style-were very definitely influential at the time and may well have altered the course of the investigation of these problems. As Sammy Eilenberg explains, the next big influence on Elgot's thinking was category theory, which gave him a way of expressing his ideas in a sharply algebraic manner. The joint book with Eilenberg is one illustration of this influence.
Author | : Peter Aczel |
Publisher | : Cambridge University Press |
Total Pages | : 320 |
Release | : 1992 |
Genre | : Computers |
ISBN | : 9780521414135 |
The lecture courses in this work are derived from the SERC 'Logic for IT' Summer School and Conference on Proof Theory held at Leeds University. The contributions come from acknowledged experts and comprise expository and research articles; put together in this book they form an invaluable introduction to proof theory that is aimed at both mathematicians and computer scientists.
Author | : Robert S. Cohen |
Publisher | : Springer Science & Business Media |
Total Pages | : 969 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 9400993498 |
The decision to undertake this volume was made in 1971 at Lake Como during the Varenna summer school ofthe Italian Physical Society, where Professor Leon Rosenfeld was lecturing on the history of quantum theory. We had long been struck by the unique blend of epistemological, histori cal and social concerns in his work on the foundations and development of physics, and decided to approach him there with the idea of publishing a collection of his papers. He responded enthusiastically, and agreed to help us select the papers; furthermore, he also agreed to write a lengthy introduction and to comment separately on those papers that he felt needed critical re-evaluation in the light of his current views. For he was still vigorously engaged in both theoretical investigations of, and critical not reflections on the foundations of theoretical physics. We certainly did conceive of the volume as a memorial to a 'living saint', but rather more practically, as a useful tool to place in the hands of fellow workers and students engaged in wrestling with these difficult problems. All too sadly, fate has added a memorial aspect to our labors. We agreed that in order to make this book most useful for the con temporary community of physicists and philosophers, we should trans late all non-English items into English.
Author | : Vincent F. Hendricks |
Publisher | : Springer Science & Business Media |
Total Pages | : 345 |
Release | : 2013-03-09 |
Genre | : Philosophy |
ISBN | : 9401727961 |
hiS volume in the Synthese Library Series is the result of a conference T held at the University of Roskilde, Denmark, October 31st-November 1st, 1997. The aim was to provide a forum within which philosophers, math ematicians, logicians and historians of mathematics could exchange ideas pertaining to the historical and philosophical development of proof theory. Hence the conference was called Proof Theory: History and Philosophical Significance. To quote from the conference abstract: Proof theory was developed as part of Hilberts Programme. According to Hilberts Programme one could provide mathematics with a firm and se cure foundation by formalizing all of mathematics and subsequently prove consistency of these formal systems by finitistic means. Hence proof theory was developed as a formal tool through which this goal should be fulfilled. It is well known that Hilbert's Programme in its original form was unfeasible mainly due to Gtldel's incompleteness theorems. Additionally it proved impossible to formalize all of mathematics and impossible to even prove the consistency of relatively simple formalized fragments of mathematics by finitistic methods. In spite of these problems, Gentzen showed that by extending Hilbert's proof theory it would be possible to prove the consistency of interesting formal systems, perhaps not by finitis tic methods but still by methods of minimal strength. This generalization of Hilbert's original programme has fueled modern proof theory which is a rich part of mathematical logic with many significant implications for the philosophy of mathematics.
Author | : Ulrich Kohlenbach |
Publisher | : Springer Science & Business Media |
Total Pages | : 539 |
Release | : 2008-05-23 |
Genre | : Mathematics |
ISBN | : 3540775331 |
This is the first treatment in book format of proof-theoretic transformations - known as proof interpretations - that focuses on applications to ordinary mathematics. It covers both the necessary logical machinery behind the proof interpretations that are used in recent applications as well as – via extended case studies – carrying out some of these applications in full detail. This subject has historical roots in the 1950s. This book for the first time tells the whole story.
Author | : Ralf Schindler |
Publisher | : Walter de Gruyter |
Total Pages | : 495 |
Release | : 2013-05-02 |
Genre | : Philosophy |
ISBN | : 3110324903 |
On the occasion of the retirement of Wolfram Pohlers the Institut für Mathematische Logik und Grundlagenforschung of the University of Münster organized a colloquium and a workshop which took place July 17 – 19, 2008. This event brought together proof theorists from many parts of the world who have been acting as teachers, students and collaborators of Wolfram Pohlers and who have been shaping the field of proof theory over the years. The present volume collects papers by the speakers of the colloquium and workshop; and they produce a documentation of the state of the art of contemporary proof theory.
Author | : S.R. Buss |
Publisher | : Elsevier |
Total Pages | : 823 |
Release | : 1998-07-09 |
Genre | : Mathematics |
ISBN | : 0080533183 |
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.