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First-Order Logic

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ISBN-10: 0486683702

ISBN-13: 9780486683706

Edition: 1995 (Unabridged)

Authors: Raymond Smullyan

List price: $10.95
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Description:

An introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods.
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Book details

List price: $10.95
Copyright year: 1995
Publisher: Dover Publications, Incorporated
Publication date: 1/30/1995
Binding: Paperback
Pages: 176
Size: 5.50" wide x 8.50" long x 0.50" tall
Weight: 0.396
Language: English

Propositional Logic from the Viewpoint of Analytic Tableaux
Preliminaries &nbsp&nbsp
Foreword on Trees &nbsp&nbsp
Formulas of Propositional Logic &nbsp&nbsp
Boolean Valuations and Truth Sets
Analytic Tableaux &nbsp&nbsp
The Method of Tableaux &nbsp&nbsp
Consistency and Completeness of the System
Compactness &nbsp&nbsp
Analytic Proofs of the Compactness Theorem &nbsp&nbsp
Maximal Consistency: Lindenbaum's Construction &nbsp&nbsp
An Analytic Modification of Lindenbaum's Proof &nbsp&nbsp
The Compactness Theorem for Deducibility
First-Order Logic
First-Order Logic
Preliminaries &nbsp&nbsp
Formulas of Quantification Theory &nbsp&nbsp
First-Order Valuations and Models &nbsp&nbsp
Boolean Valuations vs. First-Order Valuations
First-Order Analytic Tableaux &nbsp&nbsp
Extension of Our Unified Notation &nbsp&nbsp
Analytic Tableaux for Quantification Theory &nbsp&nbsp
The Completeness Theorem &nbsp&nbsp
The Skolem-Lowenheim and Compactness Theorems for First-Order Logic
A Unifying Principle &nbsp&nbsp
Analytic Consistency &nbsp&nbsp
Further Discussion of Analytic Consistency &nbsp&nbsp
Analytic Consistency Properties for Finite Sets
The Fundamental Theorem of Quantification Theory &nbsp&nbsp
Regular Sets &nbsp&nbsp
The Fundamental Theorem &nbsp&nbsp
Analytic Tableaux and Regular Sets &nbsp&nbsp
The Liberalized Rule D
Axiom Systems for Quantification Theory &nbsp&nbsp
Foreword on Axiom Systems &nbsp&nbsp
The System Q subscript 1 &nbsp&nbsp
The Systems Q subscript 2, Q* subscript 2
Magic Sets &nbsp&nbsp
Magic Sets &nbsp&nbsp
Applications of Magic Sets
Analytic versus Synthetic Consistency Properties &nbsp&nbsp
Synthetic Consistency Properties &nbsp&nbsp
A More Direct Construction
Further Topics in First-Order Logic
Gentzen Systems &nbsp&nbsp
Gentzen Systems for Propositional Logic &nbsp&nbsp
Block Tableaux and Gentzen Systems for First-Order Logic
Elimination Theorems &nbsp&nbsp
Gentzen's Hauptsatz &nbsp&nbsp
An Abstract Form of the Hauptsatz &nbsp&nbsp
Some Applications of the Hauptsatz
Prenex Tableaux &nbsp&nbsp
Prenex Formulas &nbsp&nbsp
Prenex Tableaux
More on Gentzen Systems &nbsp&nbsp
Gentzen's Extended Hauptsatz &nbsp&nbsp
A New Form of the Extended Hauptsatz &nbsp&nbsp
Symmetric Gentzen Systems
Craig's Interpolation Lemma and Beth's Definability Theorem &nbsp&nbsp
Craig's Interpolation Lemma &nbsp&nbsp
Beth's Definability Theorem
Symmetric Completeness Theorems &nbsp&nbsp
Clashing Tableaux &nbsp&nbsp
Clashing Prenex Tableaux &nbsp&nbsp
A Symmetric Form of the Fundamental Theorem
Systems of Linear Reasoning &nbsp&nbsp
Configurations &nbsp&nbsp
Linear Reasoning &nbsp&nbsp
Linear Reasoning for Prenex Formulas &nbsp&nbsp
A System Based on the Strong Symmetric Form of the Fundamental Theorem
References
Subject index