First-order logic
| Autor principal: | |
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| Formato: | Libro |
| Idioma: | Inglés |
| Publicado: |
New York :
Dover
1995
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| Colección: | Dover books on mathematics
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| Materias: | |
| Ver en Universidad de Navarra: | https://unika.unav.edu/discovery/fulldisplay?docid=alma991001711289708016&context=L&vid=34UNAV_INST:VU1&search_scope=34UNAV_TODO&tab=34UNAV_TODO&lang=es |
Tabla de Contenidos:
- Part I. Propositional Logic from the Viewpoint of Analytic Tableaux Chapter I. Preliminaries 0. Foreword on Trees 1. Formulas of Propositional Logic 2. Boolean Valuations and Truth Sets Chapter II. Analytic Tableaux 1. The Method of Tableaux 2. Consistency and Completeness of the System Chapter III. Compactness 1. Analytic Proofs of the Compactness Theorem 2. Maximal Consistency: Lindenbaum's Construction 3. An Analytic Modification of Lindenbaum's Proof 4. The Compactness Theorem for Deducibility Part II. First-Order Logic Chapter IV. First-Order Logic. Preliminaries 1. Formulas of Quantification Theory 2. First-Order Valuations and Models 3. Boolean Valuations vs. First-Order Valuations Chapter V. First-Order Analytic Tableaux 1. Extension of Our Unified Notation 2. Analytic Tableaux for Quantification Theory 3. The Completeness Theorem 4. The Skolem-Lowenheim and Compactness Theorems for First-Order Logic Chapter VI. A Unifying Principle 1. Analytic Consistency 2. Further Discussion of Analytic Consistency 3. Analytic Consistency Properties for Finite Sets Chapter VII. The Fundamental Theorem of Quantification Theory 1. Regular Sets 2. The Fundamental Theorem 3. Analytic Tableaux and Regular Sets 4. The Liberalized Rule D Chapter VIII. Axiom Systems for Quantification Theory 0. Foreword on Axiom Systems 1. The System Q subscript 1 2. The Systems Q subscript 2, Q* subscript 2 Chapter IX. Magic Sets 1. Magic Sets 2. Applications of Magic Sets Chapter X. Analytic versus Synthetic Consistency Properties 1. Synthetic Consistency Properties 2. A More Direct Construction Part III. Further Topics in First-Order Logic Chapter XI. Gentzen Systems 1. Gentzen Systems for Propositional Logic 2. Block Tableaux and Gentzen Systems for First-Order Logic Chapter XII. Elimination Theorems 1. Gentzen's Hauptsatz 2. An Abstract Form of the Hauptsatz 3. Some Applications of the Hauptsatz Chapter XIII. Prenex Tableaux 1. Prenex Formulas 2. Prenex Tableaux Chapter XIV. More on Gentzen Systems 1. Gentzen's Extended Hauptsatz 2. A New Form of the Extended Hauptsatz 3. Symmetric Gentzen Systems Chapter XV. Craig's Interpolation Lemma and Beth's Definability Theorem 1. Craig's Interpolation Lemma 2. Beth's Definability Theorem Chapter XVI. Symmetric Completeness Theorems 1. Clashing Tableaux 2. Clashing Prenex Tableaux 3. A Symmetric Form of the Fundamental Theorem Chapter XVII. Systems of Linear Reasoning 1. Configurations 2. Linear Reasoning 3. Linear Reasoning for Prenex Formulas 4. A System Based on the Strong Symmetric Form of the Fundamental Theorem References Subject index
