First-order Logic

Front Cover
Courier Dover Publications, 1995 - Mathematics - 158 pages
3 Reviews

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.

  

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Review: First-Order Logic

User Review  - Peter - Goodreads

Still working on this. The kind of book that makes you feel the lights coming on and the gears starting to spin. Read full review

Review: First-Order Logic

User Review  - Timon Karnezos - Goodreads

You want to know the nitty-gritty of FOL? Smullyan's your boy. He even has some awesome puzzle books for you to put some of the arcane theory of it into practice. Read full review

Contents

II
3
III
4
IV
9
V
15
VII
25
VIII
30
IX
36
X
38
XXXIII
86
XXXIV
87
XXXV
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XXXVI
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XXXVIII
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XXXIX
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XL
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XLI
109

XI
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XV
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XXVIII
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XXX
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XXXI
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XXXII
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XLII
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XLIII
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XLIV
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XLIX
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L
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LI
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LII
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LIII
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LV
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LVII
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LVIII
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LIX
151
LX
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LXI
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LXII
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LXIII
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About the author (1995)

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

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