Computation, logic, philosophy: a collection of essays
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Beijing
Science Press u.a.
1990
|
| Schriftenreihe: | Mathematics and its application (China series)
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002706870&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XXVII, 373 S. |
| ISBN: | 7030002113 0792302184 |
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| 490 | 0 | |a Mathematics and its application (China series) | |
| 650 | 4 | |a Bibliographie Wang Hao | |
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| 650 | 4 | |a Complexité | |
| 650 | 4 | |a Complexité de calcul (Informatique) | |
| 650 | 4 | |a Décidabilité | |
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| 650 | 4 | |a Formalisation | |
| 650 | 4 | |a Informatique | |
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| 650 | 4 | |a Langue chinoise | |
| 650 | 7 | |a Logica |2 gtt | |
| 650 | 4 | |a Logique mathématique | |
| 650 | 4 | |a Logique symbolique et mathématique | |
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Datensatz im Suchindex
| DE-BY-TUM_call_number | 0020 0006 A 1390 |
|---|---|
| DE-BY-TUM_katkey | 796247 |
| DE-BY-TUM_location | Mag |
| DE-BY-TUM_media_number | 040006116623 |
| _version_ | 1821930824896872449 |
| adam_text | CONTENTS
INTRODUCTION xi
PART ONE. BROAD ISSUES 1
1. ON FORMALIZATION 3
1.1 Systematization [1955(53)] 3
1.2 Communication 4
1.3 Clarity and consolidation 5
1.4 Rigour 6
1.5 Approximation to intuition 7
1.6 Application to philosophy 8
1.7 Too many digits 9
1.8 Ideal language 10
1.9 How artificial language? 11
1.10 The paradoxes 12
2. THE CONCEPT OF COMPUTABILITY [(1953)] 13
2.1 Formalizing intuitive concepts 13
2.2 The intuitive concept of computability 13
2.3 Computation by theoretical machines 15
2.4 General recursive functions 15
2.5 Constructive proofs 17
2.6 Effective methods 19
2.7 Speed functions 20
2.8 Transfinite recursions 22
2.9 The indeterminate domain of computable functions 25
3. PROCESS AND EXISTENCE IN MATHEMATICS [1961(60)] 30
4. LOGIC, COMPUTATION AND PHILOSOPHY [1971(66)] 47
4.1 Logic and logical positivism 47
4.2 What is mathematics? 48
4.3 Logic and computation 50
4.4 Relatively undecidable propositions and absolutely unsolvable
problems 51
4.5 Foundations of set theory 53
4.6 What is mathematics? (continued) 56
vii
yjjj Computation, Logic, Philosophy
PART TWO. AUTOMATED THEOREM PROVEVG(ATP) 61
5. COMPUTER THEOREM PROVING AND ARTIFICIAL
INTELLIGENCE [1984(82)] 63
APPENDIX: CITATION FOR HAOWANG AS WINNER OF
MILESTONE AWARD IN AUTOMATIC THEOREM
PROVING 75
6. PROVING THEOREMS BY PATTERN RECOGNITION, I
[1960(59)] 76
6.1 Introduction 76
6.2 A program that does 9 chapters of Principia in 9 minutes 83
6.3 The EtA case solved with sequential tables 94
6.4 General remarks 96
7. OBSERVATIONS ON ATP 103
7.1 Mechanical mathematics and inferential analysis [1963(61)] 103
7.2 The mechanization of mechanical arguments [I963(62)a] 118
7.3 Formalization and automatic theorem—proving [1965(64)]
127
8. SOME DATA FOR ATP 139
8.1 On axioms of conditional set existence [1967(66)] „ 139
8.2 Natural hulls and set existence [l%7(66)a] 143
8.3 A theorem on definitions of the Zermelo Neumann ordinals
[I967(66)b] 149
9. PROVING THEOREMS BY PATTERN RECOGNITION, II
[1961(60)a] 159
9.1 A survey of the decision problem 159
9.2 The Skolem, case 167
9.3 The A2E satisfiability case 174
9.4 The AiEiAj satisfiability case 176
9.5 A proof procedure for the predicate calculus 186
9.6 Remarks on mathematical disciplines 189
PART THREE. DECIDABILITY AND COMPLEXITY 193
10. GAMES, LOGIC AND COMPUTERS [l965a] 195
APPENDIX: NOTES ON A CLASS OF TILING PROBLEMS
[1975(60)] 209
Contents :.,
11. DOMINOES AND THE AEA CASE OF THE DECISION
PROBLEM [1963(62)] 218
12. TOWARDS FEASIBLE SOLUTIONS OF THE TAUTOLOGY
PROBLEM (with B.Dunhan) [1976(74)] 246
12.1 Computational complexity and Boolean validity 246
12.2 A brief overview with some general observations 248
12.3 Some basic properties of Boolean validity 252
12.4 Some calculations and classifications 257
12.5 Hard examples and negative results 263
12.6 A feasible decision procedure for biconditional expressions 266
12.7 Two partial methods and an indication of two generic methods
269
13. RANKED MATCHING AND HOSPITAL INTERNS
(with D.A.Martin) [(1977)] 275
13.1 Preliminary 275
13.2 Deletion of useless names: Operations I and II 276
13.3 The canonical form Ti of T 278
13.4 The student and hospital optimal assignments 280
13.5 Mixed assignments and a characterization of all stable
assignments 284
13.6 The marriage problem 286
PART FOUR. TOPICS FROM THEORY TO PRACTICE 291
14. LOGICAL FRAGMENTS RELEVANT TO COMPUTER
SCIENCE 293
14.1 Logic of many sorted theories [1952(50)] 293
14.2 Ackermann s consistency proof [1962(53)] 304
14.3 Partial systems of number theory [1962(55)] 314
14.4 The calculus of partial predicates and its extension to set
theory [1961(61)] 319
14.5 Model theory [1974(71)] 325
15. COMPUTERS AND MATHEMATICAL ACTIVITY 331
15.1 Remarks on machines, sets and the decision problem
[1964(63)] 331
15.2 Logic and computers [1965] 344
15.3 Remarks on mathematics and computers [1970(67)] 349
15.4 On the long range prospects of automatic theorem proving
[l970(68)a] 355
16. ON INFORMATION PROCESSING OF THE CHINESE
LANGUAGE [1979] 361
x Computation, Logic, Philosophy
THE LIST OF THE PUBLICATIONS OF THE AUTHOR 371
Note. The numbers in square brackets refer to the list of References at the end of
the Introduction. The first number refers to the year when the material was published
for the first time, and the second number, in paratheses, refers to the year when it was
written. For instance, [1955(53)] means that the item was written in 1953 and
published initially in 1955.
|
| any_adam_object | 1 |
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| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| format | Book |
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| indexdate | 2024-12-20T08:17:04Z |
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| isbn | 7030002113 0792302184 |
| language | English |
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| physical | XXVII, 373 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
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| spellingShingle | Wang, Hao Computation, logic, philosophy a collection of essays Bibliographie Wang Hao Calculabilité Complexité Complexité de calcul (Informatique) Décidabilité Décidabilité (Logique mathématique) Démonstration automatique Filosofia e fundamentos da matematica larpcal Formalisation Informatique Informatique - Mathématiques ram Langue chinoise Logica gtt Logique mathématique Logique symbolique et mathématique Logique symbolique et mathématique ram Philosophie mathématique Théorèmes - Démonstration automatique Wiskunde gtt Informatik Logik Mathematik Computer science Mathematics Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd Logik (DE-588)4036202-4 gnd Computer (DE-588)4070083-5 gnd Informatik (DE-588)4026894-9 gnd |
| subject_GND | (DE-588)4037951-6 (DE-588)4036202-4 (DE-588)4070083-5 (DE-588)4026894-9 |
| title | Computation, logic, philosophy a collection of essays |
| title_auth | Computation, logic, philosophy a collection of essays |
| title_exact_search | Computation, logic, philosophy a collection of essays |
| title_full | Computation, logic, philosophy a collection of essays Wang Hao |
| title_fullStr | Computation, logic, philosophy a collection of essays Wang Hao |
| title_full_unstemmed | Computation, logic, philosophy a collection of essays Wang Hao |
| title_short | Computation, logic, philosophy |
| title_sort | computation logic philosophy a collection of essays |
| title_sub | a collection of essays |
| topic | Bibliographie Wang Hao Calculabilité Complexité Complexité de calcul (Informatique) Décidabilité Décidabilité (Logique mathématique) Démonstration automatique Filosofia e fundamentos da matematica larpcal Formalisation Informatique Informatique - Mathématiques ram Langue chinoise Logica gtt Logique mathématique Logique symbolique et mathématique Logique symbolique et mathématique ram Philosophie mathématique Théorèmes - Démonstration automatique Wiskunde gtt Informatik Logik Mathematik Computer science Mathematics Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd Logik (DE-588)4036202-4 gnd Computer (DE-588)4070083-5 gnd Informatik (DE-588)4026894-9 gnd |
| topic_facet | Bibliographie Wang Hao Calculabilité Complexité Complexité de calcul (Informatique) Décidabilité Décidabilité (Logique mathématique) Démonstration automatique Filosofia e fundamentos da matematica Formalisation Informatique Informatique - Mathématiques Langue chinoise Logica Logique mathématique Logique symbolique et mathématique Philosophie mathématique Théorèmes - Démonstration automatique Wiskunde Informatik Logik Mathematik Computer science Mathematics Logic, Symbolic and mathematical Mathematische Logik Computer |
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Bibliotheksmagazin
| Signatur: |
0020 0006 A 1390 Lageplan |
|---|---|
| Exemplar 1 | Ausleihbar Am Standort |