Holdings: Finite model theory

Finite model theory:

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Bibliographic Details
Main Authors:	Ebbinghaus, Heinz-Dieter 1939- (Author), Flum, Jörg 1944- (Author)
Format:	Book
Language:	German
Published:	Berlin [u.a.] Springer 2006
Edition:	2., rev. and enl. ed.
Series:	Springer monographs in mathematics
Subjects:	Lógica matemática Teoria dos modelos Model theory Modelltheorie Endliche Modelltheorie
Online Access:	Inhaltsverzeichnis
Item Description:	Literaturverz. S. 339 - 347
Physical Description:	XI, 360 S. graph. Darst.
ISBN:	9783540287872

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MARC


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Record in the Search Index

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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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author	Ebbinghaus, Heinz-Dieter 1939- Flum, Jörg 1944-
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edition	2., rev. and enl. ed.
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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
work_keys_str_mv	AT ebbinghausheinzdieter finitemodeltheory AT flumjorg finitemodeltheory

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