First-Order Logic

I. Propositional Logic from the Viewpoint of Analytic Tableaux.- I. Preliminaries.- x0. Foreword on Trees.- x1. Formulas of Propositional Logic.- x2. Boolean Valuations and Truth Sets.- II. Analytic Tableaux.- x1. The Method of Tableaux.- x2. Consistency and Completeness of the System.- III. Compactness.- x1. Analytic Proofs of the Compactness Theorem.- x2. Maximal Consistency: Lindenbaum's Construction.- x3. An Analytic Modification of Lindenbaum's Proof.- x4. The Compactness Theorem for Deducibility.- II. First-Order Logic.- IV. First-Order Logic. Preliminaries.- x1. Formulas of Quantification Theory.- x2. First-Order Valuations and Models.- x3. Boolean Valuations vs. First-Order Valuations.- V. First-Order Analytic Tableaux.- x1. Extension of Our Unified Notation.- x2. Analytic Tableaux for Quantification Theory.- x3. The Completeness Theorem.- x4. The Skolem-Lowenheim and Compactness Theorems for First-Order Logic.- VI. A Unifying Principle.- x1. Analytic Consistency.- x2. Further Discussion of Analytic Consistency.- x3. Analytic Consistency Properties for Finite Sets.- VII. The Fundamental Theorem of Quantification Theory.- x1. Regular Sets.- x2. The Fundamental Theorem.- x3. Analytic Tableaux and Regular Sets.- x4. The Liberalized Rule D.- VIII. Axiom Systems for Quantification Theory.- x0. Foreward on Axiom Systems.- x1. The System Q1.- x2. The Systems Q2, Q*2.- IX. Magic Sets.- x1. Magic Sets.- x2. Applications of Magic Sets.- X. Analytic versus Synthetic Consistency Properties.- x1. Synthetic Consistency Properties.- x2. A More Direct Construction.- III. Further Topics in First-Order Logic.- XI. Gentzen Systems.- x1. Gentzen Systems for Propositional Logic.- x2. Block Tableaux and Gentzen Systems for First-Order Logic.- XII. Elimination Theorems.- x1. Gentzen's Hauptsatz.- x2. An Abstract Form of the Hauptsatz Ill.- x3. Some Applications of the Hauptsatz.- XIII. Prenex Tableaux.- x1. Prenex Formulas.- x2. Prenex Tableaux.- XIV. More on Gentzen Systems.- x1. Gentzen's Extended Hauptsatz.- x2. A New Form of the Extended Hauptsatz.- x3. Symmetric Gentzen Systems.- XV. Craig's Interpolation Lemma and Beth's Definability Theorem.- x1. Craig's Interpolation Lemma.- x2. Beth's Definability Theorem.- XVI. Symmetric Completeness Theorems.- x1. Clashing Tableaux.- x2. Clashing Prenex Tableaux.- x3. A Symmetric Form of the Fundamental Theorem.- XVII. Systems of Linear Reasoning.- x1. Configurations.- x2. Linear Reasoning.- x3. Linear Reasoning for Prenex Formulas.- x4. A System Based on the Strong Symmetrie Form of the Fundamental Theorem.- References.

著者

Smullyan, Raymond R.

出版社

Springer-Verlag Berlin and Heidelberg GmbH & Co. K

発売日

2012-04-14

価格

価格未定（税込・書誌情報提供：openBD）

ISBN

9783642867200

ページ数

176ページ

発売済み