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Applied Proof Theory: Proof Interpretations and their Use in Mathematics

2008-05-23 Mathematics
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Release : 2008-05-23
Genre : Mathematics
Kind : eBook
Book Rating : 331/5 ( reviews)

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Book Synopsis Applied Proof Theory: Proof Interpretations and their Use in Mathematics by : Ulrich Kohlenbach

Download or read book Applied Proof Theory: Proof Interpretations and their Use in Mathematics written by Ulrich Kohlenbach. This book was released on 2008-05-23. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Proof Theory and Automated Deduction

2001-11-30 Computers
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Release : 2001-11-30
Genre : Computers
Kind : eBook
Book Rating : 684/5 ( reviews)

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Book Synopsis Proof Theory and Automated Deduction by : Jean Goubault-Larrecq

Download or read book Proof Theory and Automated Deduction written by Jean Goubault-Larrecq. This book was released on 2001-11-30. Available in PDF, EPUB and Kindle. Book excerpt: Interest in computer applications has led to a new attitude to applied logic in which researchers tailor a logic in the same way they define a computer language. In response to this attitude, this text for undergraduate and graduate students discusses major algorithmic methodologies, and tableaux and resolution methods. The authors focus on first-order logic, the use of proof theory, and the computer application of automated searches for proofs of mathematical propositions. Annotation copyrighted by Book News, Inc., Portland, OR

Proof Theory

2009-06-10 Mathematics
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Release : 2009-06-10
Genre : Mathematics
Kind : eBook
Book Rating : 250/5 ( reviews)

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Book Synopsis Proof Theory by : Wolfram Pohlers

Download or read book Proof Theory written by Wolfram Pohlers. This book was released on 2009-06-10. Available in PDF, EPUB and Kindle. Book excerpt: Although this is an introductory text on proof theory, most of its contents is not found in a unified form elsewhere in the literature, except at a very advanced level. The heart of the book is the ordinal analysis of axiom systems, with particular emphasis on that of the impredicative theory of elementary inductive definitions on the natural numbers. The "constructive" consequences of ordinal analysis are sketched out in the epilogue. The book provides a self-contained treatment assuming no prior knowledge of proof theory and almost none of logic. The author has, moreover, endeavoured not to use the "cabal language" of proof theory, but only a language familiar to most readers.

Dag Prawitz on Proofs and Meaning

2014-11-27 Philosophy
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Release : 2014-11-27
Genre : Philosophy
Kind : eBook
Book Rating : 411/5 ( reviews)

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Book Synopsis Dag Prawitz on Proofs and Meaning by : Heinrich Wansing

Download or read book Dag Prawitz on Proofs and Meaning written by Heinrich Wansing. This book was released on 2014-11-27. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Proof Theory

1998-07-09 Mathematics
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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.

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