First-order Logic

Copertina anteriore
Courier Corporation, 1 gen 1995 - 158 pagine

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.

 

Sommario

II
3
III
4
IV
9
V
15
VII
25
VIII
30
IX
36
X
38
XXXV
86
XXXVI
87
XXXVII
89
XXXVIII
91
XL
96
XLI
99
XLII
101
XLIII
109

XI
40
XII
41
XIII
43
XV
46
XVI
51
XVII
52
XIX
53
XX
57
XXI
63
XXII
65
XXIV
67
XXV
69
XXVI
70
XXVII
71
XXVIII
73
XXIX
75
XXX
78
XXXI
79
XXXII
80
XXXIII
81
XXXIV
84
XLIV
110
XLV
111
XLVI
115
XLVII
117
XLVIII
118
XLIX
121
LI
122
LII
124
LIII
127
LIV
131
LV
133
LVII
136
LIX
141
LX
142
LXI
151
LXII
153
LXIII
154
LXIV
156
LXV
157
Copyright

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Informazioni sull'autore (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

Informazioni bibliografiche