Automated Development of Fundamental Mathematical Theories (Hardcover, 1993 ed.)

The author provides an introduction to automated reasoning, and in particular to resolution theorem proving using the prover OTTER. He presents a new clausal version of von Neumann-Bernays-Goedel set theory, and lists over 400 theorems proved semiautomatically in elementary set theory. He presents a semiautomated proof that the composition of homomorphisms is a homomorphism, thus solving a challenge problem. The author next develops Peano's arithmetic, and gives more than 1200 definitions and theorems in elementary number theory. He gives part of the proof of the fundamental theorem of arithmetic (unique factorization), and gives and OTTER-generated proof of Euler's generalization of Fermat's theorem. Next he develops Tarski's geometry within OTTER. He obtains proofs of most of the challenge problems appearing in the literature, and offers further challenges. He then formalizes the modal logic calculus K4, in order to obtain very high level automated proofs of Loeb's theorem, and of Goedel's two incompleteness theorems. Finally he offers thirty-one unsolved problems in elementary number theory as challenge problems.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Automated Reasoning Series, 2
Release date:	December 2003
First published:	November 1992
Authors:	Art Quaife
Dimensions:	234 x 156 x 17mm (L x W x T)
Format:	Hardcover
Pages:	273
Edition:	1993 ed.
ISBN-13:	978-0-7923-2021-0
Categories:	Books > Science & Mathematics > Mathematics > Mathematical foundations > Mathematical logic Promotions
LSN:	0-7923-2021-2
Barcode:	9780792320210

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