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Automated Development of Fundamental Mathematical Theories: 2 (Automated Reasoning Series) - Tapa dura
Sinopsis
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-Gödel 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 Löb's theorem, and of Gödel's two incompleteness theorems. Finally he offers thirty-one unsolved problems in elementary number theory as challenge problems.
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Críticas
` Quaife's work represents a breakthrough in automated reasoning for demonstrating that proofs of deep, well-known theorems of set theory and number theory can be mechanically derived, in a practical way, from the most elegant, simple, and general purpose foundations: set theory (a finite, first order axiomatization) and resolution (as implemented in the Otter system). '
Robert Boyer, University of Texas at Austin
Reseña del editor
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-Gödel 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 Löb's theorem, and of Gödel's two incompleteness theorems. Finally he offers thirty-one unsolved problems in elementary number theory as challenge problems.
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Automated Development of Fundamental Mathematical Theories
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Automated Development of Fundamental Mathematical Theories (Automated Reasoning Series, 2)
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Automated Development of Fundamental Mathematical Theories
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Condición: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 semiautomati. Nº de ref. del artículo: 5966663
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Automated Development of Fundamental Mathematical Theories (Hardcover)
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Kluwer Academic Publishers, Dordrecht, 1992
ISBN 10: 0792320212
ISBN 13: 9780792320210
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Hardcover. Condición: new. Hardcover. 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-Godel 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 Lob's theorem, and of Godel's two incompleteness theorems. Finally he offers thirty-one unsolved problems in elementary number theory as challenge problems. The author provides an introduction to automated reasoning, and in particular to resolution theorem proving using the prover OTTER. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Nº de ref. del artículo: 9780792320210
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Automated Development of Fundamental Mathematical Theories
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Springer Netherlands, Springer Netherlands Nov 1992, 1992
ISBN 10: 0792320212
ISBN 13: 9780792320210
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Buch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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-Gödel 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 Löb's theorem, and of Gödel's two incompleteness theorems. Finally he offers thirty-one unsolved problems in elementary number theory as challenge problems. 296 pp. Englisch. Nº de ref. del artículo: 9780792320210
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