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Symbolic logic and mechanical theorem proving
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 pr...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York,
Academic Press
[1973]
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| Colección: | Computer science and applied mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Symbolic Logic and Mechanical Theorem Proving; Copyright Page; Dedication; Table of Contents; Preface; Acknowledgments; Chapter1. Introduction; 1.1 Artificial Intelligence, Symbolic Logic, and Theorem Proving; 1.2 Mathematical Background; References; Chapter2. 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 PropositionalLogic; 2.5 Logical Consequences; 2.6 Applications of the Propositional Logic; References; Exercises.
- Chapter3. The First-Order Logic3.1 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-OrderLogic; References; Exercises; Chapter4. 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'sTheorem; 4.6 Implementation of Herbrand's Theorem; References; Exercises; Chapter5. The Resolution Principle; 5.1 Introduction; 5.2 The Resolution Principle for the Propositional Logic; 5.3 Substitution and Unification.
- 5.4 Unification Algorithm5.5 The Resolution Principle for the First-Order Logic; 5.6 Completeness of the Resolution Principle; 5.7 Examples Using the ResolutionPrinciple; 5.8 Deletion Strategy; References; Exercises; Chapter6. 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 Resolution6.8 Lock Resolution; 6.9 Completeness of LockResolution; References; Exercises; Chapter7. Linear Resolution; 7.1 Introduction; 7.2 Linear Resolution; 7.3 Input Resolution and Unit Resolution; 7.4 Linear Resolution UsingOrdered Clauses and the Information of Resolved Literals; 7.5 Completeness of Linear Resolution; 7.6 Linear Deduction and TreeSearching; 7.7 Heuristics in Tree Searching; 7.8 Estimations of Evaluation Functions; References; Exercises; Chapter8. The Equality Relation; 8.1 Introduction; 8.2 Unsatisfiability under Special Classes of Models.
- 8.3 Paramodulation-An Inference Rule for Equality8.4 Hyperparamodulation; 8.5 Input and Unit Paramodulations; 8.6 Linear Paramodulation; References; Exercises; Chapter9. 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; Chapter10. Program Analysis; 10.1 Introduction; 10.2 An Informal Discussion; 10.3 Formal D�efinitions of Programs.