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Author : G. E. Mint͡s
Publisher : Unknown
Page : 304 pages
File Size : 51,7 Mb
Release : 1992
Category : Mathematics
ISBN : UCAL:B4502336
Author : Grigorii E. Mints
Publisher : North-Holland
Page : 294 pages
File Size : 40,8 Mb
Release : 1992-01-01
Category : Electronic
ISBN : 0444896198
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 : Calvin C. Elgot
Publisher : Springer Science & Business Media
Page : 475 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461381778
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,Harold Simmons,Stanley S. Wainer
Publisher : Cambridge University Press
Page : 320 pages
File Size : 49,8 Mb
Release : 1992
Category : Computers
ISBN : 052141413X
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 : Thorsten Altenkirch,Wolfgang Naraschewski,Bernhard Reus
Publisher : Springer
Page : 212 pages
File Size : 41,8 Mb
Release : 2003-06-29
Category : Computers
ISBN : 9783540481676
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 : Samuel R. Buss,Petr Hájek,Pavel Pudlák
Publisher : Cambridge University Press
Page : 128 pages
File Size : 49,9 Mb
Release : 2017-03-30
Category : Mathematics
ISBN : 9781108618489
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 thirteenth publication in the Lecture Notes in Logic series, collects the proceedings of the European Summer Meeting of the Association for Symbolic Logic held at the University of Economics in Prague, August 9–15, 1988. It includes surveys and research from preeminent logicians. The papers in this volume range over all areas of mathematical logic, including proof theory, set theory, model theory, computability theory and philosophy. This book will be of interest to all students and researchers in mathematical logic.
Author : Vincent F. Hendricks,Stig Andur Pedersen,Klaus Frovin Jørgensen
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 51,6 Mb
Release : 2013-03-09
Category : Philosophy
ISBN : 9789401727969
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 : Robert S. Cohen,J.J. Stachel
Publisher : Springer Science & Business Media
Page : 969 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400993495
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 : N. Geschwind
Publisher : Springer Science & Business Media
Page : 576 pages
File Size : 41,6 Mb
Release : 1974-10-31
Category : Language Arts & Disciplines
ISBN : 9027702624
Non-Aboriginal material.
Author : Ralf Schindler
Publisher : Walter de Gruyter
Page : 495 pages
File Size : 50,7 Mb
Release : 2013-05-02
Category : Philosophy
ISBN : 9783110324907
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 : Heinrich Wansing
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 54,9 Mb
Release : 2013-06-29
Category : Philosophy
ISBN : 9789401727983
Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.
Author : Georg Gottlob,Alexander Leitsch,Daniele Mundici
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 41,7 Mb
Release : 1997-08-13
Category : Computers
ISBN : 3540633855
This book constitutes the refereed proceedings of the 5th Kurt Gödel Colloquium on Computational Logic and Proof Theory, KGC '97, held in Vienna, Austria, in August 1997. The volume presents 20 revised full papers selected from 38 submitted papers. Also included are seven invited contributions by leading experts in the area. The book documents interdisciplinary work done in the area of computer science and mathematical logics by combining research on provability, analysis of proofs, proof search, and complexity.
Author : Ulrich Kohlenbach
Publisher : Springer Science & Business Media
Page : 539 pages
File Size : 54,5 Mb
Release : 2008-05-23
Category : Mathematics
ISBN : 9783540775331
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 : Reinhard Kahle,Michael Rathjen
Publisher : Springer
Page : 561 pages
File Size : 50,8 Mb
Release : 2015-11-02
Category : Mathematics
ISBN : 9783319101033
Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They underlie modern developments in computer science such as automated theorem proving and type theory.
Author : Heinrich Wansing
Publisher : Springer
Page : 469 pages
File Size : 44,8 Mb
Release : 2014-11-27
Category : Philosophy
ISBN : 9783319110417
This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.
