Metamathematics, Machines and Gödel's Proof (Cambridge Tracts in Theoretical Computer Science, Series Number 38) - Softcover

Shankar, N.

Softcover

ISBN 10: 0521585333 ISBN 13: 9780521585330

Publisher: Cambridge University Press, 1997

Synopsis

The automatic verification of large parts of mathematics has been an aim of many mathematicians from Leibniz to Hilbert. While Gödel'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 Gödel 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.

About this title

Book Description:

Now in paperback, this book describes the use of a computer program to check the proofs of several celebrated theorems in metamathematics including Gödel'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.

Review:

."..the main purpose of this book is to describe how the Boyer-Moore theorem prover was used to mechanically verify two landmark theorems of mathematical logic, Godel's first incompleteness theorem and the Church-Rosser theorem of the lambda calculus..for specialized collections in artificial intelligence." D.V. Feldman, Choice

About this edition

• Publisher: Cambridge University Press
• Publication date: 1997
• ISBN 10: 0521585333
• ISBN 13: 9780521585330
• Binding: Paperback
• Number of pages: 220