Automation of Reasoning

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

      PDF

   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

"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.

• Automation
• Extension
• Principia Mathematica
• Resolution
• algorithms
• automated theorem proving
• complexity
• computer proof
• heuristics
• logic
• mathematics
• proof
• proving
• theorem proving
• type theory

• 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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