Proofs and Computations | Buch

Cover: 9780521517690 | Proofs and Computations | Helmut Schwichtenberg (u. a.) | Buch | 2013

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Sprache: Englisch

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Beschreibung

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 ¿11-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 ¿11-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.

Über den Autor

Helmut Schwichtenberg is an Emeritus Professor of Mathematics at Ludwig-Maximilians-Universität München. He has recently developed the 'proof-assistant' MINLOG, a computer-implemented logic system for proof/program development and extraction of computational content.

Inhaltsverzeichnis

Preface; Preliminaries; Part I. Basic Proof Theory and Computability: 1. Logic; 2. Recursion theory; 3. Godel's theorems; Part II. Provable Recursion in Classical Systems: 4. The provably recursive functions of arithmetic; 5. Accessible recursive functions, ID<¿ and ¿11-CA0; Part III. Constructive Logic and Complexity: 6. Computability in higher types; 7. Extracting computational content from proofs; 8. Linear two-sorted arithmetic; Bibliography; Index.

Details

Erscheinungsjahr:	2013
Fachbereich:	Grundlagen
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
ISBN-13:	9780521517690
ISBN-10:	0521517699
Sprache:	Englisch
Einband:	Gebunden
Autor:	Schwichtenberg, Helmut Wainer, Stanley S.
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	240 x 161 x 33 mm
Von/Mit:	Helmut Schwichtenberg (u. a.)
Erscheinungsdatum:	28.03.2013
Gewicht:	0,969 kg