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Author : A. S. Troelstra,H. Schwichtenberg
Publisher : Cambridge University Press
Page : 436 pages
File Size : 41,7 Mb
Release : 2000-07-27
Category : Computers
ISBN : 0521779111
Introduction to proof theory and its applications in mathematical logic, theoretical computer science and artificial intelligence.
Author : Paolo Mancosu,Sergio Galvan,Richard Zach
Publisher : Oxford University Press
Page : 431 pages
File Size : 44,9 Mb
Release : 2021
Category : Philosophy
ISBN : 9780192895936
An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.
Author : Helmut Schwichtenberg,Stanley S. Wainer
Publisher : Cambridge University Press
Page : 480 pages
File Size : 53,9 Mb
Release : 2011-12-15
Category : Mathematics
ISBN : 9781139504164
Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.
Author : Peter Aczel,Harold Simmons,Stanley S. Wainer
Publisher : Cambridge University Press
Page : 320 pages
File Size : 42,5 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 : Anne Sjerp Troelstra,Helmut Schwichtenberg
Publisher : Unknown
Page : 417 pages
File Size : 45,7 Mb
Release : 2000
Category : Proof theory
ISBN : 0521784522
Introduction to proof theory and its applications in mathematical logic, theoretical computer science and artificial intelligence.
Author : Reinhard Kahle,Peter Schroeder-Heister
Publisher : Springer Science & Business Media
Page : 249 pages
File Size : 52,7 Mb
Release : 2001-09-28
Category : Computers
ISBN : 9783540427520
This book constitutes the refereed proceedings of the International Seminar on Proof Theory in Computer Science, PTCS 2001, held in Dagstuhl Castle, Germany, in October 2001. The 13 thoroughly revised full papers were carefully reviewed and selected for inclusion in the book. Among the topics addressed are higher type recursion, lambda calculus, complexity theory, transfinite induction, categories, induction-recursion, post-Turing analysis, natural deduction, implicit characterization, iterate logic, and Java programming.
Author : Martin Aigner,Günter M. Ziegler
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 41,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662223437
According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, analysis, combinatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics.
Author : Daniel J. Velleman
Publisher : Cambridge University Press
Page : 401 pages
File Size : 51,9 Mb
Release : 2006-01-16
Category : Mathematics
ISBN : 9780521861243
This new edition of Daniel J. Velleman's successful textbook contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software.
Author : Toshiyasu Arai
Publisher : Springer Nature
Page : 327 pages
File Size : 50,6 Mb
Release : 2020-08-11
Category : Philosophy
ISBN : 9789811564598
This book provides readers with a guide to both ordinal analysis, and to proof theory. It mainly focuses on ordinal analysis, a research topic in proof theory that is concerned with the ordinal theoretic content of formal theories. However, the book also addresses ordinal analysis and basic materials in proof theory of first-order or omega logic, presenting some new results and new proofs of known ones.Primarily intended for graduate students and researchers in mathematics, especially in mathematical logic, the book also includes numerous exercises and answers for selected exercises, designed to help readers grasp and apply the main results and techniques discussed.
Author : Richard H. Hammack
Publisher : Unknown
Page : 314 pages
File Size : 41,6 Mb
Release : 2016-01-01
Category : Mathematics
ISBN : 0989472116
This book is an introduction to the language and standard proof methods of mathematics. It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity.
Author : Sara Negri,Jan von Plato
Publisher : Cambridge University Press
Page : 279 pages
File Size : 51,5 Mb
Release : 2008-07-10
Category : Mathematics
ISBN : 0521068428
A concise introduction to structural proof theory, a branch of logic studying the general structure of logical and mathematical proofs.
Author : Alfred North Whitehead,Bertrand Russell
Publisher : Cambridge University Press
Page : 524 pages
File Size : 47,7 Mb
Release : 1927
Category : Mathematics
ISBN : 052106791X
The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.
Author : Rob Nederpelt,Herman Geuvers
Publisher : Cambridge University Press
Page : 465 pages
File Size : 52,5 Mb
Release : 2014-11-06
Category : Computers
ISBN : 9781107036505
A gentle introduction for graduate students and researchers in the art of formalizing mathematics on the basis of type theory.
Author : S.R. Buss
Publisher : Elsevier
Page : 810 pages
File Size : 50,9 Mb
Release : 1998-07-09
Category : 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.
Author : Andrew Wohlgemuth
Publisher : Courier Corporation
Page : 385 pages
File Size : 47,9 Mb
Release : 2014-06-10
Category : Mathematics
ISBN : 9780486141688
The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixes offer supplemental material. Teachers will welcome the return of this long-out-of-print volume, appropriate for both one- and two-semester courses.