Optimization methods for logical inference:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1999
|
| Schriftenreihe: | Wiley-Interscience series in discrete mathematics and optimization
A Wiley-Interscience publication |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 365 S. graph. Darst. |
| ISBN: | 0471570354 |
Internformat
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Datensatz im Suchindex
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| adam_text | OPTIMIZATION METHODS FOR LOGICAL INFERENCE VIJAY CHANDRU JOHN HOOKER A
WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC. NEW YORK *
CHICHESTER * WEINHEIM * BRISBANE * SINGAPORE * TORONTO CONTENTS PREFACE
XIII 1 INTRODUCTION 1 1.1 LOGIC AND MATHEMATICS: THE TWAIN SHALL MEET 3
1.2 INFERENCE METHODS FOR LOGIC MODELS 6 1.3 LOGIC MODELING MEETS
MATHEMATICAL MODELING 7 1.4 THE DIFFICULTY OF INFERENCE 8 2
PROPOSITIONAL LOGIC: SPECIAL CASES 11 2.1 BASIC CONCEPTS OF
PROPOSITIONAL LOGIC 13 2.1.1 FORMULAS 13 2.1.2 NORMAL FORMS 16 2.1.3
RULES 22 2.2 INTEGER PROGRAMMING MODELS 23 2.2.1 OPTIMIZATION AND
INFERENCE 25 2.2.2 THE LINEAR PROGRAMMING RELAXATION 27 2.3 HOERN
POLYTOPES 31 2.3.1 HOERN RESOLUTION 31 2.3.2 THE INTEGER LEAST ELEMENT OF
A HOERN POLYTOPE ... 34 2.3.3 DUAL INTEGRALITY OF HOERN POLYTOPES 37 2.4
QUADRATIC AND RENAMABLE HOERN SYSTEMS 41 2.4.1 SATISFIABILITY OF
QUADRATIC SYSTEMS 42 2.4.2 THE MEDIAN CHARACTERISTIC OF QUADRATIC
SYSTEMS . . 44 2.4.3 RECOGNIZING RENAMABLE HOERN SYSTEMS 45 2.4.4 Q-HORN
PROPOSITIONS 53 2.5 NESTED CLAUSE SYSTEMS 55 2.5.1 NESTED PROPOSITIONS:
DEFINITION AND RECOGNITION . . 55 2.5.2 MAXIMUM SATISFIABILITY OF NESTED
CLAUSE SYSTEMS 58 2.5.3 EXTENDED NESTED CLAUSE SYSTEMS 61 VN VLLL
CONTENTS 2.6 EXTENDED HOERN SYSTEMS 63 2.6.1 THE ROUNDING THEOREM 65
2.6.2 SATISFIABILITY OF EXTENDED HOERN SYSTEMS 69 2.6.3 VERIFYING
RENAMABLE EXTENDED HOERN SYSTEMS . . . . 70 2.6.4 THE UNIT RESOLUTION
PROPERTY 71 2.6.5 EXTENDED HOERN RULE BASES 73 2.7 PROBLEMS WITH INTEGRAL
POLYTOPES 76 2.7.1 BALANCED PROBLEMS 78 2.7.2 INTEGRALITY AND RESOLUTION
81 2.8 LIMITED BACKTRACKING 87 2.8.1 MAXIMUM EMBEDDED RENAMABLE HOERN
SYSTEMS ... 89 2.8.2 HIERARCHIES OF SATISFIABILITY PROBLEMS 91 2.8.3
GENERALIZED AND SPLIT HOERN SYSTEMS 94 3 PROPOSITIONAL LOGIC: THE GENERAL
CASE 97 3.1 TWO CLASSIC INFERENCE METHODS 98 3.1.1 RESOLUTION FOR
PROPOSITIONAL LOGIC 99 3.1.2 A SIMPLE BRANCHING PROCEDURE 101 3.1.3
BRANCHING RULES 103 3.1.4 IMPLEMENTATION OF A BRANCHING ALGORITHM 104
3.1.5 INCREMENTAL SATISFIABILITY 106 3.2 GENERATING HARD PROBLEMS 109
3.2.1 PIGEONHOLE PROBLEMS 110 3.2.2 PROBLEMS BASED ON GRAPHS 111 3.2.3
RANDOM PROBLEMS HARD FOR RESOLUTION 113 3.2.4 RANDOM PROBLEMS HARD FOR
BRANCHING 114 3.3 BRANCHING METHODS 116 3.3.1 BRANCH AND BOUND 117 3.3.2
JEROSLOW-WANG METHOD 121 3.3.3 HOERN RELAXATION METHOD 122 3.3.4 BOUNDED
RESOLUTION METHOD 123 3.4 TABLEAU METHODS 123 3.4.1 THE SIMPLEX METHOD
IN TABLEAU FORM 124 3.4.2 PIVOT AND COMPLEMENT 128 3.4.3 COLUMN
SUBTRACTION 131 3.5 CUTTING PLANE METHODS 133 3.5.1 RESOLVENTS AS
CUTTING PLANES 134 3.5.2 UNIT RESOLUTION AND RANK 1 CUTS 136 3.5.3 A
SEPARATION ALGORITHM FOR RANK 1 CUTS 143 3.5.4 A BRANCH-AND-CUT
ALGORITHM 144 3.5.5 EXTENDED RESOLUTION AND CUTTING PLANES 148 3.6
RESOLUTION FOR 0-1 INEQUALITIES 150 CONTENTS IX 3.6.1 INEQUALITIES AS
LOGICAL FORMULAS 153 3.6.2 A GENERALIZED RESOLUTION ALGORITHM 154 3.6.3
SOME EXAMPLES 157 3.7 A SET-COVERING FORMULATION WITH FACET CUTS 159
3.7.1 THE SET-COVERING FORMULATION 160 3.7.2 ELEMENTARY FACETS OF
SATISFIABILITY 164 3.7.3 RESOLVENT FACETS ARE PRIME IMPLICATIONS 166
3.7.4 A LIFTING TECHNIQUE FOR GENERAL FACETS 171 3.8 A NONLINEAR
PROGRAMMING APPROACH 173 3.8.1 FORMULATION AS A NONLINEAR PROGRAMMING
PROBLEM 174 3.8.2 AN INTERIOR POINT ALGORITHM 175 3.8.3 A SATISFIABILITY
HEURISTIC 176 3.9 TAUTOLOGY CHECKING IN LOGIC CIRCUITS 177 3.9.1 THE
TAUTOLOGY CHECKING PROBLEM 177 3.9.2 SOLUTION BY BENDERS DECOMPOSITION
179 3.9.3 LOGICAL INTERPRETATION OF THE BENDERS ALGORITHM . . 182 3.9.4
A NONNUMERIC ALGORITHM 185 3.9.5 IMPLEMENTATION ISSUES 188 3.10
INFERENCE AS PROJECTION 189 3.10.1 THE LOGICAL PROJECTION PROBLEM 191
3.10.2 COMPUTING LOGICAL PROJECTIONS BY RESOLUTION . . . . 191 3.10.3
PROJECTING HOERN CLAUSES 193 3.10.4 THE POLYHEDRAL PROJECTION PROBLEM 193
3.10.5 INFERENCE BY POLYHEDRAL PROJECTION 195 3.10.6 RESOLUTION AND
FOURIER-MOTZKIN ELIMINATION 196 3.10.7 UNIT RESOLUTION AND POLYHEDRAL
PROJECTION 197 3.10.8 COMPLEXITY OF INFERENCE BY POLYHEDRAL PROJECTION
198 3.11 OTHER APPROACHES 199 4 PROBABILISTIC AND RELATED LOGICS 203 4.1
PROBABILISTIC LOGIC 205 4.1.1 A LINEAR PROGRAMMING MODEL 206 4.1.2
SENSITIVITY ANALYSIS 209 4.1.3 COLUMN GENERATION TECHNIQUES 211 4.1.4
POINT VALUES VERSUS INTERVALS 216 4.2 BAYESIAN LOGIC 218 4.2.1 POSSIBLE
WORLD SEMANTICS FOR BAYESIAN NETWORKS . . 220 4.2.2 USING COLUMN
GENERATION WITH BENDERS DECOMPOSITION 224 X CONTENTS 4.2.3 LIMITING THE
NUMBER OF INDEPENDENCE CONSTRAINTS . 227 4.3 DEMPSTER-SHAFER THEORY 235
4.3.1 BASIC IDEAS OF DEMPSTER-SHAFER THEORY 236 4.3.2 A LINEAR MODEL OF
BELIEF FUNCTIONS 239 4.3.3 A SET-COVERING MODEL FOR DEMPSTER S
COMBINATION RULE 240 4.3.4 INCOMPLETE BELIEF FUNCTIONS 244 4.3.5
DEMPSTER-SHAFER THEORY VS. PROBABILISTIC LOGIC . . . 246 4.3.6 A
MODIFICATION OF DEMPSTER S COMBINATION RULE . . 248 4.4 CONFIDENCE
FACTORS IN RULE SYSTEMS 250 4.4.1 CONFIDENCE FACTORS 251 4.4.2 A
GRAPHICAL MODEL OF CONFIDENCE FACTOR CALCULATION 254 4.4.3 JEROSLOW S
REPRESENTABILITY THEOREM 259 4.4.4 A MIXED INTEGER MODEL FOR CONFIDENCE
FACTORS . . . 262 5 PREDICATE LOGIC 267 5.1 BASIC CONCEPTS OF PREDICATE
LOGIC 269 5.1.1 FORMULAS 269 5.1.2 INTERPRETATIONS 270 5.1.3 SKOLEM
NORMAL FORM 271 5.1.4 HERBRAND S THEOREM 274 5.2 PARTIAL INSTANTIATION
METHODS 275 5.2.1 PARTIAL INSTANTIATION 276 5.2.2 A PRIMAL APPROACH TO
AVOIDING BLOCKAGE 278 5.2.3 A DUAL APPROACH TO AVOIDING BLOCKAGE 284 5.3
A METHOD BASED ON HYPERGRAPHS 287 5.3.1 A HYPERGRAPH MODEL FOR
PROPOSITIONAL LOGIC . . . . 288 5.3.2 SHORTEST PATHS IN B-GRAPHS 290
5.3.3 EXTENSION TO UNIVERSALLY QUANTIFIED LOGIC 290 5.3.4 ANSWERING
QUERIES 295 5.4 AN INFINITE 0-1 PROGRAMMING MODEL 295 5.4.1 INFINITE
DIMENSIONAL 0-1 PROGRAMMING 296 5.4.2 A COMPACTNESS THEOREM 297 5.4.3
HERBRAND THEORY AND INFINITE 0-1 PROGRAMS 298 5.4.4 MINIMUM SOLUTIONS
299 5.5 THE LOGIC OF ARITHMETIC 301 5.5.1 DECISION METHODS FOR
ARITHMETIC 301 5.5.2 QUANTITATIVE METHODS FOR PRESBURGER REAL ARITHMETIC
302 5.5.3 QUANTITATIVE METHODS FOR PRESBURGER (INTEGER) ARITHMETIC 304
CONTENTS XI 6 NONCLASSICAL AND MANY-VALUED LOGICS 307 6.1 NONMONOTONIC
LOGICS 308 6.2 MANY-VALUED LOGICS 311 6.3 MODAL LOGICS 314 6.4
CONSTRAINT LOGIC PROGRAMMING 316 6.4.1 SOME DEFINITIONS 318 6.4.2
THEEMBEDDING 319 6.4.3 INFINITE LINEAR PROGRAMS 321 6.4.4 INFINITE 0-1
MIXED INTEGER PROGRAMS 323 APPENDIX. LINEAR PROGRAMMING 325 POLYHEDRAL
CONES 325 CONVEX POLYHEDRA 326 OPTIMIZATION AND DUAL LINEAR PROGRAMS 330
COMPLEXITY OF LINEAR PROGRAMMING 331 BIBLIOGRAPHY 333 INDEX 358
|
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| language | English |
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| spelling | Chandru, Vijay Verfasser (DE-588)1055711651 aut Optimization methods for logical inference Vijay Chandru ; John Hooker New York [u.a.] Wiley 1999 XI, 365 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley-Interscience series in discrete mathematics and optimization A Wiley-Interscience publication Kombinatorische Optimierung (DE-588)4031826-6 gnd rswk-swf Mathematische Logik (DE-588)4037951-6 gnd rswk-swf Logischer Schluss (DE-588)4139983-3 gnd rswk-swf Optimierung (DE-588)4043664-0 gnd rswk-swf Logischer Schluss (DE-588)4139983-3 s Optimierung (DE-588)4043664-0 s DE-604 Kombinatorische Optimierung (DE-588)4031826-6 s Mathematische Logik (DE-588)4037951-6 s Hooker, John 1949- Verfasser (DE-588)141218991 aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017419358&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chandru, Vijay Hooker, John 1949- Optimization methods for logical inference Kombinatorische Optimierung (DE-588)4031826-6 gnd Mathematische Logik (DE-588)4037951-6 gnd Logischer Schluss (DE-588)4139983-3 gnd Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4031826-6 (DE-588)4037951-6 (DE-588)4139983-3 (DE-588)4043664-0 |
| title | Optimization methods for logical inference |
| title_auth | Optimization methods for logical inference |
| title_exact_search | Optimization methods for logical inference |
| title_full | Optimization methods for logical inference Vijay Chandru ; John Hooker |
| title_fullStr | Optimization methods for logical inference Vijay Chandru ; John Hooker |
| title_full_unstemmed | Optimization methods for logical inference Vijay Chandru ; John Hooker |
| title_short | Optimization methods for logical inference |
| title_sort | optimization methods for logical inference |
| topic | Kombinatorische Optimierung (DE-588)4031826-6 gnd Mathematische Logik (DE-588)4037951-6 gnd Logischer Schluss (DE-588)4139983-3 gnd Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Kombinatorische Optimierung Mathematische Logik Logischer Schluss Optimierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017419358&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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