Ebook: Automation of Reasoning: 2: Classical Papers on Computational Logic 1967–1970

"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.

---

---

Content:
Front Matter....Pages I-XII
Automated Theorem Proving 1965–1970....Pages 1-24
Front Matter....Pages 25-25
A Cancellation Algorithm for Elementary Logic....Pages 27-47
An Inverse Method for Establishing Deducibility of Nonprenex Formulas of the Predicate Calculus....Pages 48-54
Automatic Theorem Proving With Renamable and Semantic Resolution....Pages 55-65
The Concept of Demodulation in Theorem Proving....Pages 66-81
Front Matter....Pages 83-83
Resolution with Merging....Pages 85-101
On Simplifying the Matrix of a WFF....Pages 102-116
Mechanical Theorem-Proving by Model Elimination....Pages 117-134
The Generalized Resolution Principle....Pages 135-151
New Directions in Mechanical Theorem Proving....Pages 152-158
AUTOMATH, a Language for Mathematics....Pages 159-200
Front Matter....Pages 201-201
Semi-Automated Mathematics....Pages 203-216
Semantic Trees in Automatic Theorem-Proving....Pages 217-232
A Simplified Format for the Model Elimination Theorem-Proving Procedure....Pages 233-248
Theorem-Provers Combining Model Elimination and Resolution....Pages 249-263
Relationship between Tactics of the Inverse Method and the Resolution Method....Pages 264-272
E-Resolution: Extension of Resolution to Include the Equality Relation....Pages 273-280
Front Matter....Pages 281-281
Commentary by the Author and Corrections....Pages 283-297
Paramodulation and Theorem-Proving in First-Order Theories with Equality....Pages 298-313
Front Matter....Pages 315-315
Completeness Results for E-Resolution....Pages 317-320
Front Matter....Pages 315-315
A Linear Format for Resolution With Merging and a New Technique for Establishing Completeness....Pages 321-330
The Unit Proof and the Input Proof in Theorem Proving....Pages 331-341
Simple Word Problems in Universal Algebras....Pages 342-376
The Case for Using Equality Axioms in Automatic Demonstration....Pages 377-398
A Linear Format for Resolution....Pages 399-416
An Interactive Theorem-Proving Program....Pages 417-434
Refinement Theorems in Resolution Theory....Pages 435-465
On the Complexity of Derivation in Propositional Calculus....Pages 466-483
Front Matter....Pages 485-485
Resolution in Type Theory....Pages 487-507
Splitting and Reduction Heuristics in Automatic Theorem Proving....Pages 508-530
A Computer Algorithm for the Determination of Deducibility on the Basis of the Inverse Method....Pages 531-541
Linear Resolution with Selection Function....Pages 542-577
Maximal Models and Refutation Completeness: Semidecision Procedures in Automatic Theorem Proving....Pages 578-608
Back Matter....Pages 609-640

---

Content:
Front Matter....Pages I-XII
Automated Theorem Proving 1965–1970....Pages 1-24
Front Matter....Pages 25-25
A Cancellation Algorithm for Elementary Logic....Pages 27-47
An Inverse Method for Establishing Deducibility of Nonprenex Formulas of the Predicate Calculus....Pages 48-54
Automatic Theorem Proving With Renamable and Semantic Resolution....Pages 55-65
The Concept of Demodulation in Theorem Proving....Pages 66-81
Front Matter....Pages 83-83
Resolution with Merging....Pages 85-101
On Simplifying the Matrix of a WFF....Pages 102-116
Mechanical Theorem-Proving by Model Elimination....Pages 117-134
The Generalized Resolution Principle....Pages 135-151
New Directions in Mechanical Theorem Proving....Pages 152-158
AUTOMATH, a Language for Mathematics....Pages 159-200
Front Matter....Pages 201-201
Semi-Automated Mathematics....Pages 203-216
Semantic Trees in Automatic Theorem-Proving....Pages 217-232
A Simplified Format for the Model Elimination Theorem-Proving Procedure....Pages 233-248
Theorem-Provers Combining Model Elimination and Resolution....Pages 249-263
Relationship between Tactics of the Inverse Method and the Resolution Method....Pages 264-272
E-Resolution: Extension of Resolution to Include the Equality Relation....Pages 273-280
Front Matter....Pages 281-281
Commentary by the Author and Corrections....Pages 283-297
Paramodulation and Theorem-Proving in First-Order Theories with Equality....Pages 298-313
Front Matter....Pages 315-315
Completeness Results for E-Resolution....Pages 317-320
Front Matter....Pages 315-315
A Linear Format for Resolution With Merging and a New Technique for Establishing Completeness....Pages 321-330
The Unit Proof and the Input Proof in Theorem Proving....Pages 331-341
Simple Word Problems in Universal Algebras....Pages 342-376
The Case for Using Equality Axioms in Automatic Demonstration....Pages 377-398
A Linear Format for Resolution....Pages 399-416
An Interactive Theorem-Proving Program....Pages 417-434
Refinement Theorems in Resolution Theory....Pages 435-465
On the Complexity of Derivation in Propositional Calculus....Pages 466-483
Front Matter....Pages 485-485
Resolution in Type Theory....Pages 487-507
Splitting and Reduction Heuristics in Automatic Theorem Proving....Pages 508-530
A Computer Algorithm for the Determination of Deducibility on the Basis of the Inverse Method....Pages 531-541
Linear Resolution with Selection Function....Pages 542-577
Maximal Models and Refutation Completeness: Semidecision Procedures in Automatic Theorem Proving....Pages 578-608
Back Matter....Pages 609-640
....