FIRST ORDER LOGIC BY RAYMOND M SMULLYAN PDF

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.

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Popular Features. Home Learning. Categories: Mathematical Logic. First-order Logic. Description 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 illustrations. Other books in this series. Introduction to Topology Bert Mendelson.

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Introduction to Graph Theory Richard J. Game Theory Morton D. Mathematics for the Non-mathematician Morris Kline. Linear Algebra Georgi E. Differential Geometry Erwin Kreyszig. Calculus Morris Kline. Probability Theory Iu. Introductory Real Analysis A. Number Theory George E. Table of contents Part I.

Preliminaries 0. Foreword on Trees 1. Formulas of Propositional Logic 2. Analytic Tableaux 1. The Method of Tableaux 2. Compactness 1. Analytic Proofs of the Compactness Theorem 2. Maximal Consistency: Lindenbaum's Construction 3. An Analytic Modification of Lindenbaum's Proof 4. 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. A Unifying Principle 1. Analytic Consistency 2. Further Discussion of Analytic Consistency 3. The Fundamental Theorem of Quantification Theory 1. Regular Sets 2. The Fundamental Theorem 3. Analytic Tableaux and Regular Sets 4. Axiom Systems for Quantification Theory 0.

Foreword on Axiom Systems 1. The System Q subscript 1 2. Magic Sets 1. Magic Sets 2. Applications of Magic Sets Chapter X. Analytic versus Synthetic Consistency Properties 1. Synthetic Consistency Properties 2. Gentzen Systems 1. Gentzen Systems for Propositional Logic 2. Elimination Theorems 1. Gentzen's Hauptsatz 2. An Abstract Form of the Hauptsatz 3. Prenex Tableaux 1. Prenex Formulas 2.

More on Gentzen Systems 1. Gentzen's Extended Hauptsatz 2. A New Form of the Extended Hauptsatz 3. Craig's Interpolation Lemma 2. Symmetric Completeness Theorems 1. Clashing Tableaux 2. Clashing Prenex Tableaux 3. Systems of Linear Reasoning 1. Configurations 2.

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First-order Logic

We use cookies to give you the best possible experience. By using our website you agree to our use of cookies. Dispatched from the UK in 2 business days When will my order arrive? Bert Mendelson. George Gamow.

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First-Order Logic

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.

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