Mathematical logic: foundations for information science
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2010
|
| Series: | Progress in computer science and applied logic
25 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 261 S. |
| ISBN: | 9783764399764 |
Staff View
MARC
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Record in the Search Index
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| adam_text |
4.5 PROBLEM OF REPRESENTABILITY 81 CONTENTS PREFACE IX CHAPTER 1 SYNTAX
OF FIRST-ORDER LANGUAGES 1 1.1 SYMBOLS OF FIRST-ORDER LANGUAGES 4 1.2
TERMS 6 1.3 LOGICAL FORMULAS 8 1.4 FREE VARIABLES AND SUBSTITUTIONS 9
1.5 GODEI TERMS OF FORMULAS 13 1.6 PROOF BY STRUCTURAL INDUCTION 15
CHAPTER 2 MODELS OF FIRST-ORDER LANGUAGES 19 2.1 DOMAINS AND
INTERPRETATIONS 22 2.2 ASSIGNMENTS AND MODELS 24 2.3 SEMANTICS OF TERMS
24 2.4 SEMANTICS OF LOGICAL CONNECTIVE SYMBOLS 25 2.5 SEMANTICS OF
FORMULAS 27 2.6 SATISFIABILITY AND VALIDITY 30 2.7 VALID FORMULAS WITH
- 31 2.8 HINTIKKASET 33 2.9 HERBRAND MODEL 35 2.10 HERBRAND MODEL WITH
VARIABLES 38 2.11 SUBSTITUTION LEMMA 41 2.12 THEOREM OF ISOMORPHISM 42
CHAPTER 3 FORMAL INFERENCE SYSTEMS 45 3.1 G INFERENCE SYSTEM 49 3.2
INFERENCE TREES, PROOF TREES AND PROVABLE SEQUENTS 52 3.3 SOUNDNESS OF
THE G INFERENCE SYSTEM 57 3.4 COMPACTNESS AND CONSISTENCY 61 3.5
COMPLETENESS OF THE G INFERENCE SYSTEM 63 3.6 SOME COMMONLY USED
INFERENCE RALES 66 3.7 PROOF THEORY AND MODEL THEORY 68 CHAPTER 4
COMPUTABILITY & REPRESENTABILITY 71 4.1 FORMAL THEORY 72 4.2 ELEMENTARY
ARITHMETIC THEORY 74 4.3 P-KERNELONN 76 4.4 CHURCH-TURING THESIS 80
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/991246128 DIGITALISIERT
DURCH VI CONTENTS 4.6 STATES OF P-KERNEL 82 4.7 OPERATIONAL CALCULUS OF
P-KERNEL 84 4.8 REPRESENTATIONS OF STATEMENTS 86 4.9 REPRESENTABILITY
THEOREM 95 CHAPTER 5 GODEI THEOREMS 97 5.1 SELF-REFERENTIAL PROPOSITION
98 5.2 DECIDABLE SETS 100 5.3 FIXED POINT EQUATION IN * 104 5.4 GOEDEL'S
INCOMPLETENESS THEOREM 107 5.5 GOEDEL'S CONSISTENCY THEOREM 109 5.6
HALTING PROBLEM 112 CHAPTER 6 SEQUENCES OF FORMAL THEORIES 117 6.1 TWO
EXAMPLES 118 6.2 SEQUENCES OF FORMAL THEORIES 122 6.3 PROSCHEMES 125 6.4
RESOLVENT SEQUENCES 128 6.5 DEFAULT EXPANSION SEQUENCES 130 6.6 FORCING
SEQUENCES 133 6.7 DISCUSSIONS ON PROSCHEMES 136 CHAPTER 7 REVISION
CALCULUS 139 7.1 NECESSARY ANTECEDENTS OF FORMAL CONSEQUENCES 140 7.2
NEW CONJECTURES AND NEW AXIOMS 143 7.3 REFUTATION BY FACTS AND MAXIMAL
CONTRACTION 144 7.4 R-CALCULUS 146 7.5 SOME EXAMPLES 153 7.6 SPECIAL
THEORY OF RELATIVITY 155 7.7 DARWIN'S THEORY OF EVOLUTION 156 7.8
REACHABILITY OF R-CALCULUS 160 7.9 SOUNDNESS AND COMPLETENESS OF
R-CALCULUS 163 7.10 BASIC THEOREM OF TESTING 164 CHAPTER 8 VERSION
SEQUENCES 169 8.1 VERSIONS AND VERSION SEQUENCES 171 8.2 THE PROSCHEME
OPEN 172 8.3 CONVERGENCE OF THE PROSCHEME 176 8.4 COMMUTATIVITY OF THE
PROSCHEME 178 8. CONTENTS VII CHAPTER 9 INDUCTIVE INFERENCE 187 9.1
GROUND TERMS, BASIC SENTENCES, AND BASIC INSTANCES 190 9.2 INDUCTIVE
INFERENCE SYSTEM A 192 9.3 INDUCTIVE VERSIONS AND INDUCTIVE PROCESS 197
9.4 THE PROSCHEME GUINA 197 9.5 CONVERGENCE OF THE PROSCHEME GUINA 204
9.6 COMMUTATIVITY OF THE PROSCHEME GUINA 206 9.7 INDEPENDENCE OF THE
PROSCHEME GUINA 207 CHAPTER 10 WORKFLOWS FOR SCIENTIFIC DISCOVERY 209
10.1 THREE LANGUAGE ENVIRONMENTS 209 10.2 BASIC PRINCIPLES OF THE
META-LANGUAGE ENVIRONMENT 213 10.3 AXIOMATIZATION 217 10.4 FORMAL
METHODS 219 10.5 WORKFLOW OF SCIENTIFIC RESEARCH 225 APPENDIX 1 SETS AND
MAPS 229 APPENDIX 2 SUBSTITUTION LEMMA AND ITS PROOF 233 APPENDIX 3
PROOF OF THE REPRESENTABILITY THEOREM 237 A3.1 REPRESENTATION OF THE
WHILE STATEMENT IN * 237 A3.2 REPRESENTABILITY OF THE P-PROCEDURE BODY
244 BIBLIOGRAPHY 253 INDEX 257 |
| any_adam_object | 1 |
| author | Li, Wei 1943- |
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| bvnumber | BV035644403 |
| callnumber-first | Q - Science |
| callnumber-label | QA9 |
| callnumber-raw | QA9 |
| callnumber-search | QA9 |
| callnumber-sort | QA 19 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 130 ST 125 |
| classification_tum | DAT 540f |
| ctrlnum | (OCoLC)496229267 (DE-599)DNB991246128 |
| 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 |
| format | Book |
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| indexdate | 2024-12-10T09:00:57Z |
| institution | BVB |
| isbn | 9783764399764 |
| language | English |
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| physical | XII, 261 S. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| 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 - basic principles and formal calculus Mathematical logic foundations for information science Wei Li Basel [u.a.] Birkhäuser 2010 XII, 261 S. 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 978-3-7643-9977-1 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=017699138&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_alt | Mathematical logic - basic principles and formal calculus |
| 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=017699138&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004157568 |
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