| Metamathematics, Machines and Gödel's Proof Revised Edition Contributor(s): Shankar, N. (Author) |
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ISBN: 0521585333 ISBN-13: 9780521585330 Publisher: Cambridge University Press OUR PRICE: $53.19 Product Type: Paperback Published: March 1997 Annotation: The automatic verification of large parts of mathematics has been an aim of many mathematicians from Leibniz to Hilbert. While Godel'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 Godel 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. |
| Additional Information |
| BISAC Categories: - Computers | Reference - Mathematics | Logic - Computers | Programming Languages - General |
| Dewey: 511.3 |
| Series: Cambridge Tracts in Theoretical Computer Science (Paperback) |
| Physical Information: 0.52" H x 7.6" W x 9.14" (0.86 lbs) 220 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: The automatic verification of large parts of mathematics has been an aim of many mathematicians from Leibniz to Hilbert. While G 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 G 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. |