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Automation of Reasoning

2: Classical Papers on Computational Logic 1967–1970

  • Book
  • © 1983

Overview

Editors:
  1. Jörg H. Siekmann

    1. Institut für Informatik I, Universität Karlsruhe, Karlsruhe, West Germany

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  2. Graham Wrightson

    1. Department of Information Science, Victoria University, Wellington, New Zealand

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: Symbolic Computation (SYMBOLIC)

Part of the book sub series: Artificial Intelligence (1064)

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Table of contents (33 chapters)

  1. Front Matter

    Pages I-XII
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  2. Automated Theorem Proving 1965–1970

    1. Automated Theorem Proving 1965–1970

      • L. Wos, L. Henschen
      Pages 1-24

  3. 1967

    1. Front Matter

      Pages 25-25
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    2. A Cancellation Algorithm for Elementary Logic

      • R. W. Binkley, R. L. Clark
      Pages 27-47

    3. An Inverse Method for Establishing Deducibility of Nonprenex Formulas of the Predicate Calculus

      • S. Yu Maslov
      Pages 48-54

    4. Automatic Theorem Proving With Renamable and Semantic Resolution

      • J. R. Slagle
      Pages 55-65

    5. The Concept of Demodulation in Theorem Proving

      • L. T. Wos, G. A. Robinson, D. F. Carson, L. Shalla
      Pages 66-81

  4. 1968

    1. Front Matter

      Pages 83-83
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    2. Resolution with Merging

      • P. B. Andrews
      Pages 85-101

    3. On Simplifying the Matrix of a WFF

      • P. B. Andrews
      Pages 102-116

    4. Mechanical Theorem-Proving by Model Elimination

      • D. W. Loveland
      Pages 117-134

    5. The Generalized Resolution Principle

      • J. A. Robinson
      Pages 135-151

    6. New Directions in Mechanical Theorem Proving

      • J. A. Robinson
      Pages 152-158

    7. AUTOMATH, a Language for Mathematics

      • N. G. de Bruijn
      Pages 159-200

  5. 1969

    1. Front Matter

      Pages 201-201
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    2. Semi-Automated Mathematics

      • J. R. Guard, F. C. Oglesby, J. H. Bennett, L. G. Settle
      Pages 203-216

    3. Semantic Trees in Automatic Theorem-Proving

      • R. Kowalski, P. J. Hayes
      Pages 217-232

    4. A Simplified Format for the Model Elimination Theorem-Proving Procedure

      • D. W. Loveland
      Pages 233-248

    5. Theorem-Provers Combining Model Elimination and Resolution

      • D. W. Loveland
      Pages 249-263

    6. Relationship between Tactics of the Inverse Method and the Resolution Method

      • S. Yu. Maslov
      Pages 264-272
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Keywords

About this book

"Kind of crude, but it works, boy, it works!" AZan NeweZZ to Herb Simon, Christmas 1955 In 1954 a computer program produced what appears to be the first computer generated mathematical proof: Written by M. Davis at the Institute of Advanced Studies, USA, it proved a number theoretic theorem in Presburger Arithmetic. Christmas 1955 heralded a computer program which generated the first proofs of some propositions of Principia Mathematica, developed by A. Newell, J. Shaw, and H. Simon at RAND Corporation, USA. In Sweden, H. Prawitz, D. Prawitz, and N. Voghera produced the first general program for the full first order predicate calculus to prove mathematical theorems; their computer proofs were obtained around 1957 and 1958, about the same time that H. Gelernter finished a computer program to prove simple high school geometry theorems. Since the field of computational logic (or automated theorem proving) is emerging from the ivory tower of academic research into real world applications, asserting also a definite place in many university curricula, we feel the time has corne to examine and evaluate its history. The article by Martin Davis in the first of this series of volumes traces the most influential ideas back to the 'prehistory' of early logical thought showing how these ideas influenced the underlying concepts of most early automatic theorem proving programs.

Editors and Affiliations

  • Institut für Informatik I, Universität Karlsruhe, Karlsruhe, West Germany

    Jörg H. Siekmann

  • Department of Information Science, Victoria University, Wellington, New Zealand

    Graham Wrightson

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