Metamathematics, Machines and Goedel''s Proof

Klappentext Mathematicians from Leibniz to Hilbert have sought to mechanise the verification of mathematical proofs. Developments arising out of Godel's proof of his incompleteness theorem showed that no computer program could automatically prove true all the theorems of mathematics. In practice! however! there are a number of sophisticated automated reasoning programs that are quite effective at checking mathematical proofs. Now in paperback! this book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including Godel's incompleteness theorem and the Church Rosser theorem. 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 mechanisation of metamathematics itself has important implications for automated reasoning since metatheorems can be applied by labour-saving devices to simplify proof construction. The book should be accessible to scientists and philosophers with some knowledge of logic and computing. Zusammenfassung Describes the use of computer programs to check several proofs in the foundations of mathematics. 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.

Product details

• Authors: N. Shankar, N. (Sri International Shankar, Natarajan Shankar
• Assisted by: C. J. van Rijsbergen (Editor), C. J. van Rijsbergen (Editor)
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Released: 30.01.1997
• EAN: 9780521585330
• ISBN: 978-0-521-58533-0
• No. of pages: 220
• Series: Cambridge Tracts in Theoretica
• Subjects: Natural sciences, medicine, IT, technology > IT, data processing > General, dictionaries; Non-fiction book > Dictionaries, reference works > Dictionaries, encyclopaedias