Applied Proof Theory: Proof Interpretations and their Use in Mathematics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Applied Proof Theory: Proof Interpretations and their Use in Mathematics write by Ulrich Kohlenbach. This book was released on 2008-05-23. Applied Proof Theory: Proof Interpretations and their Use in Mathematics available in PDF, EPUB and Kindle. 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
Proof Theory and Automated Deduction - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proof Theory and Automated Deduction write by Jean Goubault-Larrecq. This book was released on 2001-11-30. Proof Theory and Automated Deduction available in PDF, EPUB and Kindle. 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
Dag Prawitz on Proofs and Meaning
Dag Prawitz on Proofs and Meaning - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dag Prawitz on Proofs and Meaning write by Heinrich Wansing. This book was released on 2014-11-27. Dag Prawitz on Proofs and Meaning available in PDF, EPUB and Kindle. 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.
Ordinal Analysis with an Introduction to Proof Theory
Ordinal Analysis with an Introduction to Proof Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Ordinal Analysis with an Introduction to Proof Theory write by Toshiyasu Arai. This book was released on 2020-08-11. Ordinal Analysis with an Introduction to Proof Theory available in PDF, EPUB and Kindle. 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.
Proof Theory
Proof Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proof Theory write by Wolfram Pohlers. This book was released on 2009-06-10. Proof Theory available in PDF, EPUB and Kindle. 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.
