The Classical Decision Problem

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Springer Science & Business Media, Aug 28, 2001 - Mathematics - 482 pages
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This book is addressed to all those - logicians, computer scientists, mathe maticians, philosophers of science as well as the students in all these disci plines - who may be interested in the development and current status of one of the major themes of mathematical logic in the twentieth century, namely the classical decision problem known also as Hilbert's Entscheidungsproblem. The text provides a comprehensive modern treatment of the subject, includ ing complexity theoretic analysis. We have made an effort to combine the features of a research monograph and a textbook. Only the basic knowledge of the language of first-order logic is required for understanding of the main parts of the book, and we use standard terminology. The chapters are written in such a way that various combinations of them can be used for introductory or advanced courses on undecidability, decidability and complexity of logical decision problems. This explains a few intended redundancies and repetitions in some of the chapters. The annotated bibliography, the historical remarks at the end of the chap ters and the index allow the reader to use the text also for quick reference purposes.
 

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Contents

II
1
III
5
IV
8
V
17
VI
18
VII
33
VIII
38
IX
43
LVIII
229
LIX
233
LX
239
LXI
242
LXII
247
LXIII
249
LXV
257
LXVI
261

X
44
XI
48
XII
57
XIII
66
XIV
70
XV
71
XVI
74
XVII
77
XVIII
78
XIX
81
XX
85
XXI
87
XXIII
91
XXIV
98
XXV
109
XXVI
115
XXVII
124
XXIX
130
XXX
131
XXXI
135
XXXII
137
XXXIII
143
XXXIV
146
XXXV
149
XXXVI
150
XXXVII
159
XXXVIII
161
XXXIX
163
XL
171
XLI
178
XLII
186
XLIII
188
XLIV
189
XLV
190
XLVII
198
XLVIII
202
XLIX
205
L
210
LI
216
LII
219
LIII
220
LIV
223
LV
227
LVI
228
LXVII
270
LXVIII
271
LXIX
281
LXX
285
LXXI
290
LXXIII
295
LXXIV
304
LXXV
306
LXXVI
310
LXXVII
315
LXXVIII
316
LXXIX
318
LXXX
323
LXXXI
329
LXXXII
337
LXXXIII
338
LXXXIV
341
LXXXV
345
LXXXVII
348
LXXXVIII
351
LXXXIX
354
XC
357
XCI
359
XCII
360
XCIII
365
XCIV
369
XCV
370
XCVI
374
XCVII
377
XCVIII
382
XCIX
387
C
388
CI
390
CIII
393
CIV
400
CV
407
CVII
408
CVIII
410
CIX
414
CX
419
CXI
421
CXII
477
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The Logic of Knowledge Bases

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About the author (2001)

Erich Gradel is Professor for Mathematical Foundations of Computer Science at RWTH Aachen University in Germany.

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