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Cover: 9780521585330 | Metamathematics, Machines and Godel's Proof | Shankar (u. a.) | Buch
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Metamathematics, Machines and Godel's Proof
Taschenbuch von Natarajan Shankar (u. a.)
Sprache: Englisch

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Beschreibung
The automatic verification of large parts of mathematics has been an aim of many mathematicians from Leibniz to Hilbert. While Gö del's first incompleteness theorem showed that no computer program could automatically prove certain true theorems in mathematics, the advent of electronic computers and sophisticated software means in practice there are many quite effective systems for automated reasoning that can be used for checking mathematical proofs. This book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including those of Gö del and Church-Rosser. The computer verification using the Boyer-Moore theorem prover yields precise and rigorous proofs of these difficult theorems. It also demonstrates the range and power of automated proof checking technology. The mechanization of metamathematics itself has important implications for automated reasoning, because metatheorems can be applied as labor-saving devices to simplify proof construction.
The automatic verification of large parts of mathematics has been an aim of many mathematicians from Leibniz to Hilbert. While Gö del's first incompleteness theorem showed that no computer program could automatically prove certain true theorems in mathematics, the advent of electronic computers and sophisticated software means in practice there are many quite effective systems for automated reasoning that can be used for checking mathematical proofs. This book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including those of Gö del and Church-Rosser. The computer verification using the Boyer-Moore theorem prover yields precise and rigorous proofs of these difficult theorems. It also demonstrates the range and power of automated proof checking technology. The mechanization of metamathematics itself has important implications for automated reasoning, because metatheorems can be applied as labor-saving devices to simplify proof construction.
Inhaltsverzeichnis
1. Introduction; 2. The statement of the incompleteness theorem; 3. Derived inference rules; 4. The representability of metatheory; 5. The undecidable sentence; 6. A mechanical proof of the Church-Rosser theorem; 7. Conclusions.
Details
Erscheinungsjahr: 2002
Fachbereich: EDV
Genre: Informatik
Rubrik: Naturwissenschaften & Technik
Thema: Lexika
Medium: Taschenbuch
ISBN-13: 9780521585330
ISBN-10: 0521585333
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Shankar, Natarajan
Shankar, N.
Redaktion: Rijsbergen, C. J. van
Hersteller: Cambridge University Press
Maße: 235 x 191 x 12 mm
Von/Mit: Natarajan Shankar (u. a.)
Erscheinungsdatum: 08.10.2002
Gewicht: 0,42 kg
Artikel-ID: 102588009
Inhaltsverzeichnis
1. Introduction; 2. The statement of the incompleteness theorem; 3. Derived inference rules; 4. The representability of metatheory; 5. The undecidable sentence; 6. A mechanical proof of the Church-Rosser theorem; 7. Conclusions.
Details
Erscheinungsjahr: 2002
Fachbereich: EDV
Genre: Informatik
Rubrik: Naturwissenschaften & Technik
Thema: Lexika
Medium: Taschenbuch
ISBN-13: 9780521585330
ISBN-10: 0521585333
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Shankar, Natarajan
Shankar, N.
Redaktion: Rijsbergen, C. J. van
Hersteller: Cambridge University Press
Maße: 235 x 191 x 12 mm
Von/Mit: Natarajan Shankar (u. a.)
Erscheinungsdatum: 08.10.2002
Gewicht: 0,42 kg
Artikel-ID: 102588009
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