A logical theory of nonmonotonic inference and belief change:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2001
|
| Schriftenreihe: | Artificial intelligence
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 434 S. |
| ISBN: | 3540417664 9783540417668 |
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| 245 | 1 | 0 | |a A logical theory of nonmonotonic inference and belief change |c Alexander Bochman |
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Datensatz im Suchindex
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|---|---|
| adam_text | ALEXANDER BOCHMAN
A LOGICAL THEORY
O
F NONMONOTONI
C
INFERENCE AND
BELIEF CHANGE
SPRINGER
CONTENTS
1. INTRODUCTIO
N 1
PART I. TH
E FRAMEWORK
2. CONSEQUENC
E RELATION
S
13
2.1 SCOTT CONSEQUENCE RELATIONS 13
2.1.1 BASIC DEFINITIONS 13
2.1.2 REPRESENTATION THEOREM 16
2.1.3 COMPACT SETS OF THEORIES 18
2.1.4 RIGHT COMPACTNESS 19
2.1.5 DETERMINATE AND LINEAR CONSEQUENCE RELATIONS 20
2.2 TARSKI CONSEQUENCE RELATIONS 22
2.3 SUPRACLASSICALITY 25
2.3.1 SUPRACLASSICAL TARSKI CONSEQUENCE RELATIONS 25
2.3.2 CLASSICAL CONSEQUENCE RELATIONS 26
2.3.3 SEMI-CLASSICAL CONSEQUENCE RELATIONS 27
2.3.4 SUPRACLASSICAL SCOTT RELATIONS 29
2.4 GROUNDED SCOTT CONSEQUENCE RELATIONS 31
2.5 BASE-GENERATED CONSEQUENCE RELATIONS 35
2.5.1 UNION-CLOSURE AND STRONG BASE-GENERATION 38
2.5.2 BASE-GENERATED TARSKI CONSEQUENCE RELATIONS 40
3
. EPISTEMI
C STATE
S
43
3.1 GENERAL EPISTEMIC STATES 43
3.2 MAIN KINDS OF EPISTEMIC STATES 50
3.2.1 STANDARD EPISTEMIC STATES 50
3.2.2 MONOTONICITY AND ITS KINDS 51
3.2.3 PERSISTENT EPISTEMIC STATES 53
3.2.4 PURE EPISTEMIC STATES 53
3.2.5 HOMOGENEOUS AND WORLDS-BASED STATES 56
3.2.6 KINDS OF PREFERENCE ORDER 58
3.3 BASE-GENERATED EPISTEMIC STATES 59
3.3.1 GENERAL AND NORMAL BASE-GENERATION 60
VIII CONTENTS
3.4 PRIORITIZED BASE-GENERATION 62
3.4.1 COMBINING PREFERENCE RELATIONS 63
3.4.2 DEFAULT PRIORITIES 64
3.5 FLOCKS 68
3.6 NONMONOTONIC INFERENCE AND ITS KINDS 70
3.6.1 POOLE S ABDUCTIVE FRAMEWORK 70
3.6.2 SKEPTICAL INFERENCE 71
3.6.3 CONTRACTION INFERENCE 73
3.6.4 CREDULOUS INFERENCE 74
3.6.5 A DIGRESSION: CAREFUL AND ADVENTUROUS INFERENCE 75
4. SIMILARIT
Y AND DECOMPOSITIO
N
77
4.1 SIMILARITY 77
4.1.1 SIMILARITY OF PURE BASES 79
4.1.2 UNION-CLOSURE AND BASE-GENERATION 80
4.1.3 SIMILARITY OF PRIORITIZED BASES 81
4.1.4 PERSISTENCE AND FLOCK-GENERATION 83
4.2 DECOMPOSITION OF EPISTEMIC STATES 85
4.3 NORMAL SIMILARITY 89
4.4 LANGUAGE-RESTRICTED EPISTEMIC STATES 93
4.5 EQUIVALENCE 96
4.5.1 STATIC EQUIVALENCE 100
4.5.2 SKEPTICAL EQUIVALENCE 101
4.5.3 BELIEF EQUIVALENCE 103
4.6 DECOMPOSITION OF INFERENCE RELATIONS 105
4.7 SYNTACTIC CHARACTERIZATION OF INFERENCE RELATIONS 106
5. EPISTEMI
C ENTRENCHMEN
T
IL
L
5.1 EXPECTATION RELATIONS IL
L
5.2 ENTRENCHMENT, PLAUSIBILITY AND DEPENDENCE 113
5.2.1 ENTRENCHMENT RELATIONS 113
5.2.2 PLAUSIBILITY RELATIONS 115
5.2.3 DEPENDENCE RELATIONS 115
5.2.4 CORRESPONDENCES 116
5.2.5 COMPARATIVE PROBABILITY 118
5.3 REGULAR EXPECTATION RELATIONS 119
5.4 DEPENDENCE ORDERS, CONSEQUENCE RELATIONS AND
PARTIAL EPISTEMIC ENTRENCHMENT 122
5.5 QUALITATIVE EXPECTATION RELATIONS 124
5.6 MODULAR AND LINEAR EXPECTATION RELATIONS 128
5.7 BELIEF SETS AND UNDERLYING LOGICS OF EXPECTATION RELATIONS 131
5.7.1 THE INTERNAL LOGIC OF DEPENDENCE ORDERS 131
5.7.2 BELIEF SETS OF DEPENDENCE ORDERS 132
5.7.3 BELIEF SET AND LOGIC OF QUALITATIVE ENTRENCHMENT 133
CONTENTS IX
PART II
. NONMONOTONI
C INFERENCE
6. TH
E BASI
C INFERENCE RELATIO
N
137
6.1 INTRODUCTION 137
6.2 POSTULATES 139
6.3 BASIC INFERENCE VIA EXPECTATIONS 142
6.4 REGULAR INFERENCE RELATIONS 146
6.4.1 REGULARITY AND STRICT EXPECTATION RELATIONS 147
6.4.2 DUALITY 149
6.5 THE INTERNAL LOGIC OF AN INFERENCE RELATION 151
6.6 SAFE INFERENCE 156
6.7 EXTENDING THE BASIC RELATION 159
7. SKEPTICA
L INFERENCE RELATION
S
163
7.1 PREFERENTIAL INFERENCE RELATIONS 163
7.2 PREFERENTIAL INFERENCE VIA EXPECTATIONS 165
7.3 PREFERENTIAL INFERENCE AS SKEPTICAL INFERENCE 166
7.4 CONSEQUENCE-BASED INFERENCE RELATIONS 169
7.4.1 SEMI-CLASSICAL TRANSLATION 170
7.4.2 BASIC PROPOSITIONS IN NONMONOTONIC INFERENCE 171
7.5 SYNTACTIC CHARACTERIZATIONS 173
7.5.1 CONSEQUENCE RELATIONS GENERATING A SET OF CONDITIONALS. 173
7.5.2 CLASSICAL REDUCTION 176
7.5.3 BELIEF AND KNOWLEDGE CORE OF CONDITIONAL BASES 177
7.6 INFERENTIAL EQUIVALENCE 181
7.7 MODEL TRANSFORMATIONS AND REPRESENTATIVE CLASSES OF
EPISTEMIC STATES 183
7.7.1 EPISTEMIC STATES AND POSSIBLE WORLDS MODELS 183
7.7.2 PURIFICATION OF GENERAL EPISTEMIC STATES 185
7.8 BASE-GENERATED INFERENCE RELATIONS 189
7.9 INJECTIVITY AND PURE BASE-GENERATION 197
7.9.1 SYNTACTIC CHARACTERIZATIONS 203
7.10 WEAKLY RATIONAL INFERENCE 206
7.11 LINEARITY AND RATIONAL INFERENCE 207
8. DEFEASIBL
E ENTAILMEN
T
213
8.1 NONMONOTONIC META-REASONING 213
8.2 DESIDERATA FOR DEFEASIBLE ENTAILMENT 215
8.3 CONDITIONAL ENTAILMENT 222
8.4 LOCAL PRIORITIES 229
8.4.1 LOCAL DOMINANCE 233
8.5 PREFERENTIAL INHERITANCE 234
8.5.1 INHERITANCE ARGUMENTATION FRAMEWORKS 235
8.5.2 EXPANDING EXTENSIONS 239
X CONTENTS
8.5.3 THE REPRESENTATION 246
9. CREDULOU
S NONMONOTONI
C INFERENCE
251
9.1 CREDULOUS INFERENCE RELATIONS 252
9.1.1 CREDULOUS INFERENCE AND EXPECTATION RELATIONS 253
9.2 SEMANTIC REPRESENTATIONS 254
9.2.1 POSSIBLE WORLDS SEMANTICS 258
9.3 PERMISSIVE INFERENCE 260
9.4 SAFE CREDULOUS INFERENCE 264
9.5 SOME OTHER KINDS OF BRAVE INFERENCE 265
9.6 INTERRELATIONS 267
9.6.1 CREDULOUS CONDITIONALS AS DEFAULT ASSUMPTIONS 268
10
. CONTRACTIO
N INFERENCE
271
10.1 CONTRACTION INFERENCE RELATIONS 271
10.1.1 POSTULATES OF CONTRACTION INFERENCE 272
10.1.2 THE INTERNAL LOGIC OF CONTRACTIONS AND
THE SUCCESS POSTULATE 275
10.1.3 CONTRACTION AND EXPECTATION RELATIONS 277
10.1.4 CONTRACTION AND PREFERENTIAL INFERENCE 279
10.1.5 INFERENCE-EQUIVALENT CONTRACTIONS 280
10.1.6 SIMPLE, CONSERVATIVE AND CAUTIOUS CONTRACTIONS 282
10.2 COMPLETENESS 284
10.2.1 REPRESENTATION OF CONSERVATIVE, CAUTIOUS AND GENERAL
CONTRACTIONS : 288
10.2.2 A REFINED REPRESENTATION 291
10.2.3 POSSIBLE WORLDS SEMANTICS 292
10.3 CONTRACTION INFERENCE IN STANDARD AND PURE EPISTEMIC STATES.
. 293
10.4 DETERMINATION AND VACUITY 296
10.5 RATIONAL CONTRACTIONS 298
10.5.1 LINEAR CONTRACTIONS 305
10.5.2 SEVERE CONTRACTIONS 307
10.6 WITHDRAWALS 310
10.6.1 RATIONAL, LINEAR AND SEVERE WITHDRAWALS 312
10.7 RECOVERING CONTRACTION RELATIONS 312
10.7.1 RATIONAL RECOVERING CONTRACTIONS 316
PAR
T III
. BELIE
F CHANG
E
11
. BELIE
F CHANGE AND IT
S PROBLEM
S
321
11.1 THE PROBLEM OF BELIEF CHANGE 321
11.2 EPISTEMIC STATES AS A FRAMEWORK OF BELIEF CHANGE 327
11.2.1 AGM STATES AND BASE-GENERATED STATES 327
CONTENTS XI
11.2.2 DETERMINATION, UNION-CLOSURE, MONOTONICITY, AND
STANDARDNESS 329
11.2.3 COHERENCE VERSUS FOUNDATIONS 331
11.2.4 CHANGING EPISTEMIC STATES 335
11.3 SUMS AND CONTRACTIONS 336
11.3.1 SUMS OF EPISTEMIC STATES 337
11.3.2 CONTRACTION 338
11.4 MERGE AND EXPANSION 341
11.5 DERIVED CHANGES 342
12. CONTRACTION
S OF EPISTEMI
C STATE
S
345
12.1 DEFINITION AND PROPERTIES 345
12.1.1 CONTRACTIONS OF BASES AND FLOCKS 347
12.1.2 ABSTRACT CONTRACTION SYSTEMS 349
12.2 CONTRACTIONS OF PURE EPISTEMIC STATES 350
12.2.1 CONTRACTIONS OF CONSEQUENCE RELATIONS 351
12.2.2 CONTRACTION DYNAMICS 354
12.2.3 CONDITIONAL CONTRACTIONS 357
12.3 BELIEF CONTRACTION FUNCTIONS 358
12.3.1 POSTULATES 359
12.3.2 FAILURE AND SUCCESS 360
12.4 KINDS OF BELIEF CONTRACTIONS 364
12.4.1 DETERMINATE CONTRACTIONS 365
12.4.2 WITHDRAWALS 366
12.4.3 RECOVERING CONTRACTIONS 367
12.4.4 PURE BELIEF CONTRACTIONS 368
12.4.5 RATIONAL CONTRACTIONS 372
12.5 REFINED REPRESENTATIONS 376
13
. MERG
E AND EXPANSIO
N
379
13.1 MERGING EPISTEMIC STATES 380
13.1.1 PURE MERGE 384
13.1.2 PRIORITIZED MERGE 386
13.2 BASIC EXPANSIONS 388
13.2.1 BELIEF EXPANSIONS 390
13.2.2 PURE EXPANSION 392
13.2.3 PRIORITIZED EXPANSION 396
13.3 KNOWLEDGE EXPANSION 398
13.4 FLA
T EXPANSIONS 399
14. COMPOUN
D AND DERIVE
D CHANGE
S
403
14.1 CONSOLIDATION AND REVISION 403
14.2 BELIEF REVISION AND NONMONOTONIC INFERENCE 405
14.2.1 COMPLETENESS RESULTS 407
14.3 INFERENCE AND ENTRENCHMENT CHANGE 409
XII CONTENTS
14.3.1 INFERENCE CHANGE GENERATED BY EXPANSIONS 409
14.3.2 PRIORITIZED INFERENCE CHANGE 412
14.3.3 FLAT INFERENCE CHANGE 414
14.3.4 KNOWLEDGE-BASED INFERENCE CHANGE 416
14.4 CONSTRUCTIBILITY AND NATURAL CLASSES 417
14.4.1 NATURAL KINDS OF EPISTEMIC STATES 419
REFERENCE
S
425
INDE
X
431
|
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| id | DE-604.BV013738515 |
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| indexdate | 2024-07-09T18:51:08Z |
| institution | BVB |
| isbn | 3540417664 9783540417668 |
| language | English |
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| spelling | Bochman, Alexander Verfasser aut A logical theory of nonmonotonic inference and belief change Alexander Bochman Berlin [u.a.] Springer 2001 XII, 434 S. txt rdacontent n rdamedia nc rdacarrier Artificial intelligence Belief and doubt Beliet change Expert systems (Computer science) Nonmonotonic reasoning Nichtmonotones Schließen (DE-588)4210699-0 gnd rswk-swf Wissensrevision (DE-588)4273403-4 gnd rswk-swf Nichtmonotones Schließen (DE-588)4210699-0 s DE-604 Wissensrevision (DE-588)4273403-4 s DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009390884&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bochman, Alexander A logical theory of nonmonotonic inference and belief change Belief and doubt Beliet change Expert systems (Computer science) Nonmonotonic reasoning Nichtmonotones Schließen (DE-588)4210699-0 gnd Wissensrevision (DE-588)4273403-4 gnd |
| subject_GND | (DE-588)4210699-0 (DE-588)4273403-4 |
| title | A logical theory of nonmonotonic inference and belief change |
| title_auth | A logical theory of nonmonotonic inference and belief change |
| title_exact_search | A logical theory of nonmonotonic inference and belief change |
| title_full | A logical theory of nonmonotonic inference and belief change Alexander Bochman |
| title_fullStr | A logical theory of nonmonotonic inference and belief change Alexander Bochman |
| title_full_unstemmed | A logical theory of nonmonotonic inference and belief change Alexander Bochman |
| title_short | A logical theory of nonmonotonic inference and belief change |
| title_sort | a logical theory of nonmonotonic inference and belief change |
| topic | Belief and doubt Beliet change Expert systems (Computer science) Nonmonotonic reasoning Nichtmonotones Schließen (DE-588)4210699-0 gnd Wissensrevision (DE-588)4273403-4 gnd |
| topic_facet | Belief and doubt Beliet change Expert systems (Computer science) Nonmonotonic reasoning Nichtmonotones Schließen Wissensrevision |
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