Chin-Liang Chang, Richard Char-Tung Lee

Symbolic Logic and Mechanical Theorem Proving

• Gebundenes Buch

Produktbeschreibung

This book contains an introduction to symbolic logic and a thorough discussion of mechanical theorem proving and its applications. The book consists of three major parts. Chapters 2 and 3 constitute an introduction to symbolic logic. Chapters 4-9 introduce several techniques in mechanical theorem proving, and Chapters 10 an 11 show how theorem proving can be applied to various areas such as question answering, problem solving, program analysis, and program synthesis.

Produktdetails

• Verlag: Academic Press / Elsevier Science & Technology
• Artikelnr. des Verlages: C2009-0-22103-9
• 1973.
• Englisch
• Abmessung: 20mm x 152mm x 229mm
• Gewicht: 640g
• ISBN-13: 9780121703509
• ISBN-10: 0121703509
• Artikelnr.: 22485148

Inhaltsangabe

?Preface

Acknowledgments

1. Introduction

1.1 Artificial Intelligence, Symbolic Logic, and Theorem Proving

1.2 Mathematical Background

References

2. The Propositional Logic

2.1 Introduction

2.2 Interpretations of Formulas in the Propositional Logic

2.3 Validity and Inconsistency in the Propositional Logic

2.4 Normal Forms in the Propositional Logic

2.5 Logical Consequences

2.6 Applications of the Propositional Logic

References

Exercises

3. The First-Order Logic

3.1 Introduction

3.2 Interpretations of Formulas in the First-Order Logic

3.3 Prenex Normal Forms in the First-Order Logic

3.4 Applications of the First-Order Logic

References

Exercises

4. Herbrand's Theorem

4.1 Introduction

4.2 Skolem Standard Forms

4.3 The Herbrand Universe of a Set of Clauses

4.4 Semantic Trees

4.5 Herbrand's Theorem

4.6 Implementation of Herbrand's Theorem

References

Exercises

5. The Resolution Principle

5.1 Introduction

5.2 The Resolution Principle for the Propositional Logic

5.3 Substitution and Unification

5.4 Unification Algorithm

5.5 The Resolution Principle for the First-Order Logic

5.6 Completeness of the Resolution Principle

5.7 Examples Using the Resolution Principle

5.8 Deletion Strategy

References

Exercises

6. Semantic Resolution and Lock Resolution

6.1 Introduction

6.2 An Informal Introduction to Semantic Resolution

6.3 Formal Definitions and Examples of Semantic Resolution

6.4 Completeness of Semantic Resolution

6.5 Hyperresolution and the Set-of-Support Strategy: Special Cases of Semantic Resolution

6.6 Semantic Resolution Using Ordered Clauses

6.7 Implementation of Semantic Resolution

6.8 Lock Resolution

6.9 Completeness of Lock Resolution

References

Exercises

7. Linear Resolution

7.1 Introduction

7.2 Linear Resolution

7.3 Input Resolution and Unit Resolution

7.4 Linear Resolution Using Ordered Clauses and the Information of Resolved Literals

7.5 Completeness of Linear Resolution

7.6 Linear Deduction and Tree Searching

7.7 Heuristics in Tree Searching

7.8 Estimations of Evaluation Functions

References

Exercises

8. The Equality Relation

8.1 Introduction

8.2 Unsatisfiability under Special Classes of Models

8.3 Paramodulation-An Inference Rule for Equality

8.4 Hyperparamodulation

8.5 Input and Unit Paramodulations

8.6 Linear Paramodulation

References

Exercises

9. Some Proof Procedures Based on Herbrand's Theorem

9.1 Introduction

9.2 The Prawitz Procedure

9.3 The V-Resolution Procedure

9.4 Pseudosemantic Trees

9.5 A Procedure for Generating Closed Pseudosemantic Trees

9.6 A Generalization of the Splitting Rule of Davis and Putnam

References

Exercises

10. Program Analysis

10.1 Introduction

10.2 An Informal Discussion

10.3 Formal Definitions of Programs

10.4 Logical Formulas Describing the Execution of a Program

10.5 Program Analysis by Resolution

10.6 The Termination and Response of Programs

10.7 The Set-of-Support Strategy and the Deduction o