Mechanizing Proof Theory
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Mechanizing Proof Theory
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Author : Gianluigi Bellin
language : en
Publisher:
Release Date : 1990
Mechanizing Proof Theory written by Gianluigi Bellin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Computers categories.
In Part II we study Herbrand's Theorem in Linear Logic and the No Counterexample Interpretation in a fragment of Peano Arithmetic (section 10). As an application to Ramsey Theory we give a parametric form of the Ramsey Theorem, that generalizes the Infinite, the Finite and the Ramsey-Paris-Harrington Theorems for a fixed exponent (sections 10-13)."
Mechanizing Proof
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Author : Donald MacKenzie
language : en
Publisher: MIT Press
Release Date : 2004-01-30
Mechanizing Proof written by Donald MacKenzie and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-30 with Social Science categories.
Most aspects of our private and social lives—our safety, the integrity of the financial system, the functioning of utilities and other services, and national security—now depend on computing. But how can we know that this computing is trustworthy? In Mechanizing Proof, Donald MacKenzie addresses this key issue by investigating the interrelations of computing, risk, and mathematical proof over the last half century from the perspectives of history and sociology. His discussion draws on the technical literature of computer science and artificial intelligence and on extensive interviews with participants. MacKenzie argues that our culture now contains two ideals of proof: proof as traditionally conducted by human mathematicians, and formal, mechanized proof. He describes the systems constructed by those committed to the latter ideal and the many questions those systems raise about the nature of proof. He looks at the primary social influence on the development of automated proof—the need to predict the behavior of the computer systems upon which human life and security depend—and explores the involvement of powerful organizations such as the National Security Agency. He concludes that in mechanizing proof, and in pursuing dependable computer systems, we do not obviate the need for trust in our collective human judgment.
Handbook Of Proof Theory
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Author : S.R. Buss
language : en
Publisher: Elsevier
Release Date : 1998-07-09
Handbook Of Proof Theory written by S.R. Buss and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-09 with Mathematics categories.
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.
A Proof Theory For General Unification
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Author : W. Snyder
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Proof Theory For General Unification written by W. Snyder and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
In this monograph we study two generalizations of standard unification, E-unification and higher-order unification, using an abstract approach orig inated by Herbrand and developed in the case of standard first-order unifi cation by Martelli and Montanari. The formalism presents the unification computation as a set of non-deterministic transformation rules for con verting a set of equations to be unified into an explicit representation of a unifier (if such exists). This provides an abstract and mathematically elegant means of analysing the properties of unification in various settings by providing a clean separation of the logical issues from the specification of procedural information, and amounts to a set of 'inference rules' for unification, hence the title of this book. We derive the set of transformations for general E-unification and higher order unification from an analysis of the sense in which terms are 'the same' after application of a unifying substitution. In both cases, this results in a simple extension of the set of basic transformations given by Herbrand Martelli-Montanari for standard unification, and shows clearly the basic relationships of the fundamental operations necessary in each case, and thus the underlying structure of the most important classes of term unifi cation problems.
Mechanization Of Reasoning In A Historical Perspective
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Author :
language : en
Publisher: BRILL
Release Date : 2023-03-13
Mechanization Of Reasoning In A Historical Perspective written by and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-13 with Language Arts & Disciplines categories.
This volume is written jointly by Witold Marciszewski, who contributed the introductory and the three subsequent chapters, and Roman Murawski who is the author of the next ones - those concerned with the 19th century and the modern inquiries into formalization, algebraization and mechanization of reasonings. Besides the authors there are other persons, as well as institutions, to whom the book owes its coming into being. The study which resulted in this volume was carried out in the Historical Section of the research project Logical Systems and Algorithms for Automatic Testing of Reasoning, 1986-1990, in which participated nine Polish universities; the project was coordinated by the Department of Logic, Methodology and Philosophy of Science of the Bia??l??ystok Branch of the University of Warsaw, and supported by the Ministry of Education (some of its results are reported in (Srzednicki (Ed.) 1987). The major part of the project was focussed on the software for computer-aided theorem proving called Mizar MSE (Multi-Sorted first-order logic with Equality, reported in (Marciszewski 1994a)) due to Dr. Andrzej Trybulec. He and other colleagues deserve a grateful mention for a hands-on experience and theoretical stimulants owed to their collaboration.
Mechanical Theorem Proving In Geometries
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Author : Wen-tsün Wu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mechanical Theorem Proving In Geometries written by Wen-tsün Wu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
There seems to be no doubt that geometry originates from such practical activ ities as weather observation and terrain survey. But there are different manners, methods, and ways to raise the various experiences to the level of theory so that they finally constitute a science. F. Engels said, "The objective of mathematics is the study of space forms and quantitative relations of the real world. " Dur ing the time of the ancient Greeks, there were two different methods dealing with geometry: one, represented by the Euclid's "Elements," purely pursued the logical relations among geometric entities, excluding completely the quantita tive relations, as to establish the axiom system of geometry. This method has become a model of deduction methods in mathematics. The other, represented by the relevant work of Archimedes, focused on the study of quantitative re lations of geometric objects as well as their measures such as the ratio of the circumference of a circle to its diameter and the area of a spherical surface and of a parabolic sector. Though these approaches vary in style, have their own features, and reflect different viewpoints in the development of geometry, both have made great contributions to the development of mathematics. The development of geometry in China was all along concerned with quanti tative relations.
Symbolic Logic And Mechanical Theorem Proving
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Author : Chin-Liang Chang
language : en
Publisher: Academic Press
Release Date : 2014-06-28
Symbolic Logic And Mechanical Theorem Proving written by Chin-Liang Chang and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.
Automated Deduction Cade 12
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Author : Alan Bundy
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-06-08
Automated Deduction Cade 12 written by Alan Bundy and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-06-08 with Computers categories.
This volume contains the reviewed papers presented at the 12th International Conference on Automated Deduction (CADE-12) held at Nancy, France in June/July 1994. The 67 papers presented were selected from 177 submissions and document many of the most important research results in automated deduction since CADE-11 was held in June 1992. The volume is organized in chapters on heuristics, resolution systems, induction, controlling resolutions, ATP problems, unification, LP applications, special-purpose provers, rewrite rule termination, ATP efficiency, AC unification, higher-order theorem proving, natural systems, problem sets, and system descriptions.
Towards Mechanized Mathematical Assistants
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Author : Manuel Kauers
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-19
Towards Mechanized Mathematical Assistants written by Manuel Kauers and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-19 with Business & Economics categories.
This book constitutes the refereed proceedings of the 6th International Conference on Mathematical Knowledge Management, MKM 2007, and the 14th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2006, held in Hagenberg, Austria in June 2007 as events of the RISC Summer 2007, organized by the Research Institute for Symbolic Computation.
Rural Employment Migration And Economic Development Theoretical Issues And Empirical Evidence From Africa
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Author : Derek Byerlee
language : en
Publisher:
Release Date : 1972
Rural Employment Migration And Economic Development Theoretical Issues And Empirical Evidence From Africa written by Derek Byerlee and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Africa categories.