First-Order Logic

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.

Born in New York City in 1919, Raymond Smullyan is a philosopher and magician as well as a famous mathematician and logician. His career as a stage magician financed his undergraduate studies at the University of Chicago as well his doctoral work at Princeton. The author of several imaginative books on recreational mathematics, Smullyan is also a classical pianist.

Raymond Smullyan: The Merry Prankster
Raymond Smullyan (1919– ), mathematician, logician, magician, creator of extraordinary puzzles, philosopher, pianist, and man of many parts. The first Dover book by Raymond Smullyan was First-Order Logic (1995). Recent years have brought a number of his magical books of logic and math puzzles: The Lady or the Tiger (2009); Satan, Cantor and Infinity (2009); an original, never-before-published collection, King Arthur in Search of His Dog and Other Curious Puzzles (2010); and Set Theory and the Continuum Problem (with Melvin Fitting, also reprinted by Dover in 2010). More will be coming in subsequent years.

In the Author's Own Words:
"Recently, someone asked me if I believed in astrology. He seemed somewhat puzzled when I explained that the reason I don't is that I'm a Gemini."

"Some people are always critical of vague statements. I tend rather to be critical of precise statements: they are the only ones which can correctly be labeled 'wrong.'" — Raymond Smullyan

Critical Acclaim for The Lady or the Tiger:
"Another scintillating collection of brilliant problems and paradoxes by the most entertaining logician and set theorist who ever lived." — Martin Gardner

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

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Summary

Author Biography

Table of Contents

Supplemental Materials