First-order Logic

前表紙
Courier Corporation, 1995/01/01 - 158 ページ

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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... Analytic Tableaux § 1. The Method of Tableaux . § 2. Consistency and Completeness of the System Chapter III ... Properties for Finite Sets Chapter VII . The Fundamental Theorem of Quantification Theory . § 1. Regular Sets . §2 ...
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... 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 101 §1 . Gentzen Systems for ...
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目次

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

XI
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XII
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XV
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XVI
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XIX
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XX
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XXI
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XXV
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XXVI
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XXVIII
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XXIX
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XXX
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XXXI
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XXXII
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XXXIII
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XXXIV
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XLIV
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XLV
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XLVI
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XLVII
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XLVIII
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XLIX
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LI
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LII
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LIII
127
LIV
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LV
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LVII
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LIX
141
LX
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LXI
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LXII
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LXIII
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LXIV
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LXV
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著作権

他の版 - すべて表示

First-Order Logic
Raymond R. Smullyan
限定表示 - 2012
First-order Logic
Raymond M. Smullyan
限定表示 - 1995
First-order Logic
Raymond M. Smullyan
スニペット表示 - 1995
すべて表示 »

多く使われている語句

4-consistent a₁ a₂ analytic consistency property analytic tableaux atomic valuation atomically closed axiom scheme axiom system B₁ block tableau Boolean descendant Boolean valuation C₁ called Chapter clashing pair closed tableau closes with weight completeness proof completeness theorem concludes the proof configuration conjugate consider construction define dyadic tree E-complete equivalent finite set finite subset First-Order Logic free occurrence Fundamental Theorem Gentzen hence Hintikka set Hintikka's lemma induction inference rules infinite interpolation formula Interpolation Lemma interpretation k₁ König's lemma magic set maximally consistent mean modus ponens negation obvious occur open branch order valuation P₁ prenex normal form prenex sentences propositional logic propositional variable prove Q₁ Quantification Theory regular set S₁ S₂ sequent signed formulas successor Suppose systematic tableau tableau method tautology term true truth value truth-functional truth-functionally implied truth-functionally satisfiable unsatisfiable unsigned valid weak subformula weight k₂ X₁ Y₁

著者について (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

書誌情報

書籍名First-order Logic
Dover books on advanced mathematics
Dover books on mathematics
著者Raymond M. Smullyan
版イラスト付き, 完全版, 再版
出版社Courier Corporation, 1995
ISBN0486683702, 9780486683706
ページ数158 ページ
  
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