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First-Order Logic and Automated Theorem Proving /
There are many kinds of books on formal logic. Some have philosophers as their intended audience, some mathematicians, some computer scien tists. Although there is a common core to all such books, they will be very different in emphasis, methods, and even appearance. This book is intended for compu...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York, NY :
Springer New York,
1996.
|
| Edición: | Second edition. |
| Colección: | Graduate texts in computer science.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1 Background
- 2 Propositional Logic
- 2.1 Introduction
- 2.2 Propositional Logic--Syntax
- 2.3 Propositional Logic--Semantics
- 2.4 Boolean Valuations
- 2.5 The Replacement Theorem
- 2.6 Uniform Notation
- 2.7 König's Lemma
- 2.8 Normal Forms
- 2.9 Normal Form Implementations
- 3 Semantic Tableaux and Resolution
- 3.1 Propositional Semantic Tableaux
- 3.2 Propositional Tableaux Implementations
- 3.3 Propositional Resolution
- 3.4 Soundness
- 3.5 Hintikka's Lemma
- 3.6 The Model Existence Theorem
- 3.7 Tableau and Resolution Completeness
- 3.8 Completeness With Restrictions
- 3.9 Propositional Consequence
- 4 Other Propositional Proof Procedures
- 4.1 Hilbert Systems
- 4.2 Natural Deduction
- 4.3 The Sequent Calculus
- 4.4 The Davis-Putnam Procedure
- 4.5 Computational Complexity
- 5 First-Order Logic
- 5.1 First-Order Logic--Syntax
- 5.2 Substitutions
- 5.3 First-Order Semantics
- 5.4 Herbrand Models
- 5.5 First-Order Uniform Notation
- 5.6 Hintikka's Lemma
- 5.7 Parameters
- 5.8 The Model Existence Theorem
- 5.9 Applications
- 5.10 Logical Consequence
- 6 First-Order Proof Procedures
- 6.1 First-Order Semantic Tableaux
- 6.2 First-Order Resolution
- 6.3 Soundness
- 6.4 Completeness
- 6.5 Hilbert Systems
- 6.6 Natural Deduction and Gentzen Sequents
- 7 Implementing Tableaux and Resolution
- 7.1 What Next
- 7.2 Unification
- 7.3 Unification Implemented
- 7.4 Free-Variable Semantic Tableaux
- 7.5 A Tableau Implementation
- 7.6 Free-Variable Resolution
- 7.7 Soundness
- 7.8 Free-Variable Tableau Completeness
- 7.9 Free-Variable Resolution Completeness
- 8 Further First-Order Features
- 8.1 Introduction
- 8.2 The Replacement Theorem
- 8.3 Skolemization
- 8.4 Prenex Form
- 8.5 The AE-Calculus
- 8.6 Herbrand's Theorem
- 8.7 Herbrand's Theorem, Constructively
- 8.8 Gentzen's Theorem
- 8.9 Cut Elimination
- 8.10 Do Cuts Shorten Proofs?
- 8.11 Craig's Interpolation Theorem
- 8.12 Craig's Interpolation Theorem--Constructively
- 8.13 Beth's Definability Theorem
- 8.14 Lyndon's Homomorphism Theorem
- 9 Equality
- 9.1 Introduction
- 9.2 Syntax and Semantics
- 9.3 The Equality Axioms
- 9.4 Hintikka's Lemma
- 9.5 The Model Existence Theorem
- 9.6 Consequences
- 9.7 Tableau and Resolution Systems
- 9.8 Alternate Tableau and Resolution Systems
- 9.9 A Free-Variable Tableau System With Equality
- 9.10 A Tableau Implementation With Equality
- 9.11 Paramodulation
- References.