Mathematical logic: foundations for information science
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2014
|
| Edition: | 2., rev. ed. |
| Series: | Progress in computer science and applied logic
25 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 301 S. graph. Darst. |
| ISBN: | 9783034808613 |
Staff View
MARC
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| 245 | 1 | 0 | |a Mathematical logic |b foundations for information science |c Wei Li |
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Record in the Search Index
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| adam_text |
CONTENTS
PREFACE IX
PREFACE TO THE SECOND EDITION XIII
I ELEMENTS OF MATHEMATICAL LOGIC 1
1 SYNTAX OF FIRST-ORDER LANGUAGES 3
1.1 SYMBOLS OF FIRST-ORDER LANGUAGES 6
1.2 TERMS 8
1.3 LOGICAL FORMULAS 9
1.4 FREE VARIABLES AND SUBSTITUTIONS 11
1.5 GODEL TERMS OF FORMULAS 15
1.6 PROOF BY STRUCTURAL INDUCTION 17
2 MODELS OF FIRST-ORDER LANGUAGES 23
2.1 DOMAINS AND INTERPRETATIONS 26
2.2 ASSIGNMENTS AND MODELS 28
2.3 SEMANTICS OF TERMS 28
2.4 SEMANTICS OF LOGICAL CONNECTIVE SYMBOLS 29
2.5 SEMANTICS OF FORMULAS 31
2.6 SATISFIABILITY AND VALIDITY 34
2.7 VALID FORMULAS WITH -F4- 35
2.8 HERBRAND UNIVERSE, HERBRAND BASE AND HERBRAND SET 37
2.9 HERBRAND MODEL 39
2.10 HERBRAND MODEL WITH VARIABLES* 43
2.11 SUBSTITUTION LEMMA 45
2.12 THEOREM OF ISOMORPHISM 50
3 FORMAL INFERENCE SYSTEMS 55
3.1 G INFERENCE SYSTEM 59
3.2 INFERENCE TREES, PROOF TREES AND PROVABLE SEQUENTS 62
3.3 SOUNDNESS OF THE G INFERENCE SYSTEM 68
3.4 COMPLETENESS OF THE G INFERENCE SYSTEM 72
3.5 CONSISTENCY AND COMPACTNESS 75
3.6 SOME COMMONLY-USED INFERENCE RULES 77
3.7 PROOF THEORY AND MODEL THEORY 79
HTTP://D-NB.INFO/1053175345
VI CONTENTS
4 COMPUTABILITY & REPRESENTABILITY 83
4.1 FORMAL THEORY 84
4.2 THEORY OF ELEMENTARY ARITHMETIC 86
4.3 P-KERNEL ON N 89
4.4 CHURCH-TURING THESIS 92
4.5 THE PROBLEM OF REPRESENTABILITY 94
4.6 THE STATES OF P-KERNEL 95
4.7 OPERATIONAL CALCULUS OF P-KERNEL 97
4.8 REPRESENTATIONS OF STATEMENTS 99
4.8.1 THE REPRESENTATION OF THE ASSIGNMENT STATEMENT 100
4.8.2 REPRESENTATION OF THE SEQUENTIAL STATEMENT 102
4.8.3 REPRESENTATION OF THE IF STATEMENT 103
4.8.4 REPRESENTATION OF THE WHILE STATEMENT 104
4.8.5 REPRESENTATION OF THE CALL STATEMENT 112
4.9 REPRESENTABILITY THEOREM 114
5 GODEL THEOREMS 117
5.1 A SELF-REFERENTIAL PROPOSITION 118
5.2 DECIDABLE SETS 120
5.3 FIXED POINT EQUATION IN II 124
5.4 GODEL'S INCOMPLETENESS THEOREM 127
5.5 GODEL'S CONSISTENCY THEOREM 129
5.6 HALTING PROBLEM 132
II LOGICAL FRAMEWORK OF SCIENTIFIC DISCOVERY 137
6 SEQUENCES OF FORMAL THEORIES 139
6.1 TWO EXAMPLES 140
6.2 SEQUENCES OF FORMAL THEORIES 144
6.3 PROSCHEMES 148
6.4 RESOLVENT SEQUENCES 150
6.5 DEFAULT EXTENSION SEQUENCES 153
6.6 FORCING SEQUENCES 156
6.7 JUSTIFICATION FOR PROSCHEMES 159
7 REVISION CALCULUS 161
7.1 NECESSARY ANTECEDENTS OF FORMAL CONSEQUENCES 162
7.2 NEW CONJECTURES AND NEW AXIOMS 166
7.3 REFUTATION BY FACTS AND MAXIMAL CONTRACTION 166
7.4 R-CALCULUS 169
7.5 REACHABILITY, SOUNDNESS AND COMPLETENESS OF R-CALCULUS 178
7.6 ON THE LOGICAL FRAMEWORK OF SCIENTIFIC DISCOVERY 184
7.6.1 SPECIAL THEORY OF RELATIVITY 186
CONTENTS VII
7.6.2 DARWIN'S THEORY OF EVOLUTION 187
7.7 THE R-CALCULUS WITHOUT CUT 191
7.7.1 THE R-CALCULUS WITHOUT CUT 194
7.7.2 EXAMPLES 197
7.7.3 REACHABILITY, SOUNDNESS AND COMPLETENESS 200
7.8 OPERATIONAL SEMANTICS FOR PROGRAM DEBUGGING 201
7.8.1 BASIC IDEAS OF PROGRAM DEBUGGING 202
7.8.2 STRUCTURAL OPERATIONAL SEMANTICS FOR THE TRACING PROCEDURE .
204
7.8.3 OPERATIONAL SEMANTICS FOR THE LOCATING PROCEDURE 207
8 VERSION SEQUENCES 217
8.1 VERSIONS AND VERSION SEQUENCES 219
8.2 THE PROSCHEME
OPEN
220
8.3 CONVERGENCE OF THE PROSCHEME 224
8.4 COMMUTATIVITY OF THE PROSCHEME 226
8.5 INDEPENDENCE OF THE PROSCHEME 228
8.6 RELIABLE PROSCHEMES 230
9 INDUCTIVE INFERENCE 235
9.1 GROUND TERMS, BASIC SENTENCES, AND BASIC INSTANCES 238
9.2 INDUCTIVE INFERENCE SYSTEM A 240
9.3 INDUCTIVE VERSIONS AND INDUCTIVE PROCESS 245
9.4 THE PROSCHEME GUINA 245
9.5 CONVERGENCE OF THE PROSCHEME
GUINA
252
9.6 COMMUTATIVITY OF THE PROSCHEME GUINA 254
10 META-LANGUAGE ENVIRONMENTS 257
10.1 THREE LANGUAGE ENVIRONMENTS 258
10.2 BASIC PRINCIPLES OF META-LANGUAGE ENVIRONMENTS 262
10.3 AXIOMATIZATION 266
10.4 FORMAL METHODS 268
10.5 WORKFLOW OF SCIENTIFIC RESEARCH 274
APPENDIX 1 SETS AND MAPS 279
APPENDIX 2 PROOF OF THE REPRESENTABILITY THEOREM 283
BIBLIOGRAPHY 293
INDEX 297 |
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| author | Li, Wei 1943- |
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| callnumber-first | Q - Science |
| callnumber-label | QA9 |
| callnumber-raw | QA9 |
| callnumber-search | QA9 |
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| callnumber-subject | QA - Mathematics |
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| ctrlnum | (OCoLC)903689158 (DE-599)BVBBV042283163 |
| dewey-full | 511.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.3 |
| dewey-search | 511.3 |
| dewey-sort | 3511.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| edition | 2., rev. ed. |
| format | Book |
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| id | DE-604.BV042283163 |
| illustrated | Illustrated |
| indexdate | 2024-12-10T09:00:57Z |
| institution | BVB |
| isbn | 9783034808613 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027720493 |
| oclc_num | 903689158 |
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| owner | DE-11 DE-92 DE-83 |
| owner_facet | DE-11 DE-92 DE-83 |
| physical | XIV, 301 S. graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in computer science and applied logic |
| series2 | Progress in computer science and applied logic |
| spelling | Li, Wei 1943- Verfasser (DE-588)1062904451 aut Mathematical logic foundations for information science Wei Li 2., rev. ed. Basel [u.a.] Birkhäuser 2014 XIV, 301 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Progress in computer science and applied logic 25 Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 s DE-604 Erscheint auch als Online-Ausgabe 978-3-0348-0862-0 Progress in computer science and applied logic 25 (DE-604)BV004157568 25 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027720493&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Li, Wei 1943- Mathematical logic foundations for information science Progress in computer science and applied logic Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| subject_GND | (DE-588)4037951-6 |
| title | Mathematical logic foundations for information science |
| title_auth | Mathematical logic foundations for information science |
| title_exact_search | Mathematical logic foundations for information science |
| title_full | Mathematical logic foundations for information science Wei Li |
| title_fullStr | Mathematical logic foundations for information science Wei Li |
| title_full_unstemmed | Mathematical logic foundations for information science Wei Li |
| title_short | Mathematical logic |
| title_sort | mathematical logic foundations for information science |
| title_sub | foundations for information science |
| topic | Logic, Symbolic and mathematical Mathematische Logik (DE-588)4037951-6 gnd |
| topic_facet | Logic, Symbolic and mathematical Mathematische Logik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027720493&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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