Finite model theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2006
|
| Ausgabe: | 2., rev. and enl. ed. |
| Schriftenreihe: | Springer monographs in mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 339 - 347 |
| Beschreibung: | XI, 360 S. graph. Darst. |
| ISBN: | 9783540287872 |
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Datensatz im Suchindex
| _version_ | 1804135117109592064 |
|---|---|
| adam_text | HEINZ-DIETER EBBINGHAUS JORG FLUM FINITE MODEL THEORY SECOND REVISED AND
ENLARGED EDITION 1999 4Q SPRINGER TABLE OF CONTENTS PREFACE V 1.
PRELIMINARIES 1 2. THE EHRENFEUCHT-FRAISSE METHOD 13 2.1 ELEMENTARY
CLASSES 13 2.2 EHRENFEUCHT S THEOREM 15 2.3 EXAMPLES AND FRAI SSE S
THEOREM 20 2.4 HANF S THEOREM 26 2.5 GAIFMAN S THEOREM 30 3. MORE ON
GAMES 37 3.1 SECOND-ORDER LOGIC *. 37 3.2 INFINITARY LOGIC: THE LOGICS
LQOU, AND L^U 40 3.3 THE LOGICS FO S AND L^ 46 3.3.1 PEBBLE GAMES 49
3.3.2 THE S-INVARIANT OF A STRUCTURE 54 3.3.3 SCOTT FORMULAS 56 3.4
LOGICS WITH COUNTING QUANTIFIERS 58 3.5 FAILURE OF CLASSICAL THEOREMS IN
THE FINITE 62 4. 0-1 LAWS 71 4.1 0-1 LAWS FOR FO AND L, W 71 4.2
PARAMETRIC CLASSES 74 4.3 UNLABELED 0-1 LAWS 77 4.3.1 APPENDIX 82 4.4
EXAMPLES AND CONSEQUENCES 84 4.5 PROBABILITIES OF MONADIC SECOND ORDER
PROPERTIES 88 5. SATISFIABILITY IN THE FINITE 95 5.1 FINITE MODEL
PROPERTY OF FO 2 95 5.2 FINITE MODEL PROPERTY OF V 2 3*-SENTENCES 99 X
TABLE OF CONTENTS 6. FINITE AUTOMATA AND LOGIC: A MICROCOSM OF FINITE
MODEL THEORY 105 6.1 LANGUAGES ACCEPTED BY AUTOMATA 105 6.2 WORD MODELS
108 6.3 EXAMPLES AND APPLICATIONS ILL 6.4 FIRST-ORDER DEFINABILITY 114
7. DESCRIPTIVE COMPLEXITY THEORY 119 7.1 SOME EXTENSIONS OF FIRST-ORDER
LOGIC 120 7.2 TURING MACHINES AND COMPLEXITY CLASSES 124 7.2.1
DIGRESSION: TRAHTENBROT S THEOREM 127 7.2.2 STRUCTURES AS INPUTS 129 7.3
LOGICAL DESCRIPTIONS OF COMPUTATIONS 133 7.4 THE COMPLEXITY OF THE
SATISFACTION RELATION 147 7.5 THE MAIN THEOREM AND SOME CONSEQUENCES 151
7.5.1 APPENDIX 162 8. LOGICS WITH FIXED-POINT OPERATORS 165 8.1
INFLATIONARY AND LEAST FIXED-POINTS 165 8.2 SIMULTANEOUS INDUCTION AND
TRANSITIVITY 177 8.3 PARTIAL FIXED-POINT LOGIC 191 8.4 FIXED-POINT
LOGICS AND L^ 198 8.4.1 THE LOGIC FO(PFP PT IME) 205 8.4.2 FIXED-POINT
LOGIC WITH COUNTING 207 8.5 FIXED-POINT LOGICS AND SECOND-ORDER LOGIC
210 8.5.1 DIGRESSION: IMPLICIT DEFINABILITY 217 8.6 TRANSITIVE CLOSURE
LOGIC 220 8.6.1 FO(DTC) FO(TC) 221 8.6.2 FO(POSTC) AND NORMAL FORMS
224 8.6.3 FO(TC) FO(LFP) 229 8.7 BOUNDED FIXED-POINT LOGIC 235 9.
LOGIC PROGRAMS 239 9.1 DATALOG 239 9.2 I-DATALOG AND P-DATALOG 245 9.3 A
PRESERVATION THEOREM 250 9.4 NORMAL FORMS FOR FIXED-POINT LOGICS 253 9.5
AN APPLICATION OF NEGATIVE FIXED-POINT LOGIC 263 9.6 HIERARCHIES OF
FIXED-POINT LOGICS 268 10. OPTIMIZATION PROBLEMS 275 10.1 POLYNOMIALLY
BOUNDED OPTIMIZATION PROBLEMS 275 10.2 APPROXIMABLE OPTIMIZATION
PROBLEMS 280 TABLE OF CONTENTS XI 11. LOGICS FOR PTIME 287 11.1 LOGICS
AND INVARIANTS 288 11.2 PTIME ON CLASSES OF STRUCTURES 295 12.
QUANTIFIERS AND LOGICAL REDUCTIONS 307 12.1 LINDSTROM QUANTIFIERS 308
12.2 PTIME AND QUANTIFIERS 314 12.3 LOGICAL REDUCTIONS 320 12.4
QUANTIFIERS AND ORACLES 330 REFERENCES 339 INDEX 349
|
| adam_txt |
HEINZ-DIETER EBBINGHAUS JORG FLUM FINITE MODEL THEORY SECOND REVISED AND
ENLARGED EDITION 1999 4Q SPRINGER TABLE OF CONTENTS PREFACE V 1.
PRELIMINARIES 1 2. THE EHRENFEUCHT-FRAISSE METHOD 13 2.1 ELEMENTARY
CLASSES 13 2.2 EHRENFEUCHT'S THEOREM 15 2.3 EXAMPLES AND FRAI'SSE'S
THEOREM 20 2.4 HANF S THEOREM 26 2.5 GAIFMAN'S THEOREM 30 3. MORE ON
GAMES 37 3.1 SECOND-ORDER LOGIC *. 37 3.2 INFINITARY LOGIC: THE LOGICS
LQOU, AND L^U 40 3.3 THE LOGICS FO S AND L^ 46 3.3.1 PEBBLE GAMES 49
3.3.2 THE S-INVARIANT OF A STRUCTURE 54 3.3.3 SCOTT FORMULAS 56 3.4
LOGICS WITH COUNTING QUANTIFIERS 58 3.5 FAILURE OF CLASSICAL THEOREMS IN
THE FINITE 62 4. 0-1 LAWS 71 4.1 0-1 LAWS FOR FO AND L, W 71 4.2
PARAMETRIC CLASSES 74 4.3 UNLABELED 0-1 LAWS 77 4.3.1 APPENDIX 82 4.4
EXAMPLES AND CONSEQUENCES 84 4.5 PROBABILITIES OF MONADIC SECOND ORDER
PROPERTIES 88 5. SATISFIABILITY IN THE FINITE 95 5.1 FINITE MODEL
PROPERTY OF FO 2 95 5.2 FINITE MODEL PROPERTY OF V 2 3*-SENTENCES 99 X
TABLE OF CONTENTS 6. FINITE AUTOMATA AND LOGIC: A MICROCOSM OF FINITE
MODEL THEORY 105 6.1 LANGUAGES ACCEPTED BY AUTOMATA 105 6.2 WORD MODELS
108 6.3 EXAMPLES AND APPLICATIONS ILL 6.4 FIRST-ORDER DEFINABILITY 114
7. DESCRIPTIVE COMPLEXITY THEORY 119 7.1 SOME EXTENSIONS OF FIRST-ORDER
LOGIC 120 7.2 TURING MACHINES AND COMPLEXITY CLASSES 124 7.2.1
DIGRESSION: TRAHTENBROT'S THEOREM 127 7.2.2 STRUCTURES AS INPUTS 129 7.3
LOGICAL DESCRIPTIONS OF COMPUTATIONS 133 7.4 THE COMPLEXITY OF THE
SATISFACTION RELATION 147 7.5 THE MAIN THEOREM AND SOME CONSEQUENCES 151
7.5.1 APPENDIX 162 8. LOGICS WITH FIXED-POINT OPERATORS 165 8.1
INFLATIONARY AND LEAST FIXED-POINTS 165 8.2 SIMULTANEOUS INDUCTION AND
TRANSITIVITY 177 8.3 PARTIAL FIXED-POINT LOGIC 191 8.4 FIXED-POINT
LOGICS AND L^ 198 8.4.1 THE LOGIC FO(PFP PT IME) 205 8.4.2 FIXED-POINT
LOGIC WITH COUNTING 207 8.5 FIXED-POINT LOGICS AND SECOND-ORDER LOGIC
210 8.5.1 DIGRESSION: IMPLICIT DEFINABILITY 217 8.6 TRANSITIVE CLOSURE
LOGIC 220 8.6.1 FO(DTC) FO(TC) 221 8.6.2 FO(POSTC) AND NORMAL FORMS
224 8.6.3 FO(TC) FO(LFP) 229 8.7 BOUNDED FIXED-POINT LOGIC 235 9.
LOGIC PROGRAMS 239 9.1 DATALOG 239 9.2 I-DATALOG AND P-DATALOG 245 9.3 A
PRESERVATION THEOREM 250 9.4 NORMAL FORMS FOR FIXED-POINT LOGICS 253 9.5
AN APPLICATION OF NEGATIVE FIXED-POINT LOGIC 263 9.6 HIERARCHIES OF
FIXED-POINT LOGICS 268 10. OPTIMIZATION PROBLEMS 275 10.1 POLYNOMIALLY
BOUNDED OPTIMIZATION PROBLEMS 275 10.2 APPROXIMABLE OPTIMIZATION
PROBLEMS 280 TABLE OF CONTENTS XI 11. LOGICS FOR PTIME 287 11.1 LOGICS
AND INVARIANTS 288 11.2 PTIME ON CLASSES OF STRUCTURES 295 12.
QUANTIFIERS AND LOGICAL REDUCTIONS 307 12.1 LINDSTROM QUANTIFIERS 308
12.2 PTIME AND QUANTIFIERS 314 12.3 LOGICAL REDUCTIONS 320 12.4
QUANTIFIERS AND ORACLES 330 REFERENCES 339 INDEX 349 |
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| discipline | Mathematik |
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| edition | 2., rev. and enl. ed. |
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| institution | BVB |
| isbn | 9783540287872 |
| language | German |
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| physical | XI, 360 S. graph. Darst. |
| publishDate | 2006 |
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| spelling | Ebbinghaus, Heinz-Dieter 1939- Verfasser (DE-588)107046857 aut Finite model theory Heinz-Dieter Ebbinghaus ; Jörg Flum 2., rev. and enl. ed. Berlin [u.a.] Springer 2006 XI, 360 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer monographs in mathematics Literaturverz. S. 339 - 347 Lógica matemática larpcal Teoria dos modelos larpcal Model theory Modelltheorie (DE-588)4114617-7 gnd rswk-swf Endliche Modelltheorie (DE-588)4615978-2 gnd rswk-swf Endliche Modelltheorie (DE-588)4615978-2 s DE-604 Modelltheorie (DE-588)4114617-7 s 1\p DE-604 Flum, Jörg 1944- Verfasser (DE-588)121343391 aut HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014633178&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ebbinghaus, Heinz-Dieter 1939- Flum, Jörg 1944- Finite model theory Lógica matemática larpcal Teoria dos modelos larpcal Model theory Modelltheorie (DE-588)4114617-7 gnd Endliche Modelltheorie (DE-588)4615978-2 gnd |
| subject_GND | (DE-588)4114617-7 (DE-588)4615978-2 |
| title | Finite model theory |
| title_auth | Finite model theory |
| title_exact_search | Finite model theory |
| title_exact_search_txtP | Finite model theory |
| title_full | Finite model theory Heinz-Dieter Ebbinghaus ; Jörg Flum |
| title_fullStr | Finite model theory Heinz-Dieter Ebbinghaus ; Jörg Flum |
| title_full_unstemmed | Finite model theory Heinz-Dieter Ebbinghaus ; Jörg Flum |
| title_short | Finite model theory |
| title_sort | finite model theory |
| topic | Lógica matemática larpcal Teoria dos modelos larpcal Model theory Modelltheorie (DE-588)4114617-7 gnd Endliche Modelltheorie (DE-588)4615978-2 gnd |
| topic_facet | Lógica matemática Teoria dos modelos Model theory Modelltheorie Endliche Modelltheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014633178&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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