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First-Order Logic (Dover Books on Mathematics)
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Item specifics
- Condition
- Release Year
- 1995
- Book Title
- First-Order Logic (Dover Books on Mathematics)
- ISBN
- 9780486683706
About this product
Product Identifiers
Publisher
Dover Publications, Incorporated
ISBN-10
0486683702
ISBN-13
9780486683706
eBay Product ID (ePID)
914362
Product Key Features
Number of Pages
176 Pages
Language
English
Publication Name
First-Order Logic
Publication Year
1995
Subject
Logic
Type
Textbook
Subject Area
Mathematics
Series
Dover Books on Mathematics Ser.
Format
Trade Paperback
Dimensions
Item Height
0.4 in
Item Weight
7.6 Oz
Item Length
8.4 in
Item Width
5.4 in
Additional Product Features
Intended Audience
College Audience
LCCN
94-039736
Illustrated
Yes
Edition Description
Unabridged edition
Table Of Content
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-Löwenheim 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
Synopsis
This completely self-contained study, widely considered the best book in the field, is intended to serve both as an introduction to quantification theory and as an exposition of new results and techniques in "analytic" or "cut-free" methods. Impressed by the simplicity and mathematical elegance of the tableau point of view, the author focuses on it here. After preliminary material on tress (necessary for the tableau method), Part I deals with propositional logic from the viewpoint of analytic tableaux, covering such topics as formulas or propositional logic, Boolean valuations and truth sets, the method of tableaux and compactness. Part II covers first-order logic, offering detailed treatment of such matters as first-order analytic tableaux, analytic consistency, quantification theory, magic sets, and analytic versus synthetic consistency properties. Part III continues coverage of first-order logic. Among the topics discussed are Gentzen systems, elimination theorems, prenex tableaux, symmetric completeness theorems, and system linear reasoning. Raymond M. Smullyan is a well-known logician and inventor of mathematical and logical puzzles. In this book he has written a stimulating and challenging exposition of first-order logic that will be welcomed by logicians, mathematicians, and anyone interested in the field., This self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in ""analytic"" or ""cut free"" methods. The focus is on the tableau point of view. Includes 144 illustrations., This self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods. The focus is on the tableau point of view. Includes 144 illustrations., Considered the best book in the field, this completely self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods. The focus in on the tableau point of view. Topics include trees, tableau method for propositional logic, Gentzen systems, more. Includes 144 illustrations.
LC Classification Number
QA9.S57 19
Item description from the seller
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- n***7 (310)- Feedback left by buyer.Past monthVerified purchaseReceived the DVD set as listed, and the used discs are in great shape! I doubt I'll be shopping for new discs much now, with sellers like this one and another I recently bought from, why buy new when the used discs work perfectly? Great price too. Set was mailed promptly, in a padded mailer with tracking. Good seller, will shop again.
- h***1 (191)- Feedback left by buyer.Past 6 monthsVerified purchaseBook is exactly as described and even better condition. Looks like brand new. Arrived 4 days before promised date, well packaged and perfectly safe. I shopped around and this was, by far, the best price. I highly recommend not only this hilarious book, but also this Ebay seller.
- s***s (11)- Feedback left by buyer.Past 6 monthsVerified purchaseThe package was shipped here fast, and the CDs were in good condition, but the case got stuck to the pamphlet inside. The seller did tell the truth in saying it was acceptable as was described, and he chose a good price for this, as it is 2 CDs that are almost 15 years old.
Seller feedback (806,667)
- n***7 (310)- Feedback left by buyer.Past monthVerified purchaseReceived the DVD set as listed, and the used discs are in great shape! I doubt I'll be shopping for new discs much now, with sellers like this one and another I recently bought from, why buy new when the used discs work perfectly? Great price too. Set was mailed promptly, in a padded mailer with tracking. Good seller, will shop again.
- h***1 (191)- Feedback left by buyer.Past 6 monthsVerified purchaseBook is exactly as described and even better condition. Looks like brand new. Arrived 4 days before promised date, well packaged and perfectly safe. I shopped around and this was, by far, the best price. I highly recommend not only this hilarious book, but also this Ebay seller.
- s***s (11)- Feedback left by buyer.Past 6 monthsVerified purchaseThe package was shipped here fast, and the CDs were in good condition, but the case got stuck to the pamphlet inside. The seller did tell the truth in saying it was acceptable as was described, and he chose a good price for this, as it is 2 CDs that are almost 15 years old.