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Mechanizing Proof

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Release : 2004-01-30
Genre : Social Science
Kind : eBook
Book Rating : 959/5 ( reviews)

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Book Synopsis Mechanizing Proof by : Donald MacKenzie

Download or read book Mechanizing Proof written by Donald MacKenzie. This book was released on 2004-01-30. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mechanizing Proof Theory

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Release : 1990
Genre : Computers
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis Mechanizing Proof Theory by : Gianluigi Bellin

Download or read book Mechanizing Proof Theory written by Gianluigi Bellin. This book was released on 1990. Available in PDF, EPUB and Kindle. Book excerpt: 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)."

Handbook of Proof Theory

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Release : 1998-07-09
Genre : Mathematics
Kind : eBook
Book Rating : 183/5 ( reviews)

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Book Synopsis Handbook of Proof Theory by : S.R. Buss

Download or read book Handbook of Proof Theory written by S.R. Buss. This book was released on 1998-07-09. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Basic Proof Theory

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Release : 2000-07-27
Genre : Computers
Kind : eBook
Book Rating : 111/5 ( reviews)

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Book Synopsis Basic Proof Theory by : A. S. Troelstra

Download or read book Basic Proof Theory written by A. S. Troelstra. This book was released on 2000-07-27. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included.

Metamathematics, Machines and Gödel's Proof

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Release : 1997-01-30
Genre : Computers
Kind : eBook
Book Rating : 330/5 ( reviews)

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Book Synopsis Metamathematics, Machines and Gödel's Proof by : N. Shankar

Download or read book Metamathematics, Machines and Gödel's Proof written by N. Shankar. This book was released on 1997-01-30. Available in PDF, EPUB and Kindle. Book excerpt: Describes the use of computer programs to check several proofs in the foundations of mathematics.

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