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Tables of Contents for Handbook of Logic in Artificial Intelligence and Logic Programming
Chapter/Section Title
Page #
Page Count
List of contributors
xix
AI and Nonmonotonic Reasoning
1
34
Matthew L. Ginsberg
Overview
1
3
Uses of nonmonotonic reasoning
4
6
Inheritance hierarchies
4
1
Closed-world databases
5
2
Diagnosis
7
1
Reasoning about action
8
1
Database updates
9
1
Other applications
9
1
The nature of nonmonotonic reasoning
10
9
The rules of the game
10
4
Properties of default rules
14
3
Properties of default arguments
17
1
Objections to nonmonotonic inference
18
1
Conflicting default rules
19
5
Examples
20
1
Prioritization and stratification
21
2
Valour and caution
23
1
Formal approaches to nonmonotonic inference
24
2
Numeric approaches
24
1
Symbolic approaches
25
1
Practical import
26
9
Useful applications
26
1
Implementation considerations
27
1
The need for experimentation
28
7
General Patterns in Nonmonotonic Reasoning
35
76
David Makinson
Looking for a perspective
35
7
The diversity of nonmonotonic reasoning
35
2
Levels of comparison
37
2
Perspectives of this chapter
39
3
Basic theory: conditions on inference relations
42
11
Pure conditions
42
3
Interaction with truth-functional connectives
45
7
Extension families
52
1
Basic example: how their inference relations behave
53
39
Defeasible inheritance nets
54
3
Default systems
57
8
Maxiconsistent sets
65
6
Preferential models
71
12
Limiting probability evaluations
83
4
A tabular recapitulation and general discussion
87
5
Further explorations
92
19
Non-Horn conditions on inference relations
92
5
Plausibility valuations
97
3
Canonical extensions to the infinite case
100
3
Varying background sets
103
8
Some Direct Theories of Nonmonotonic Inheritance
111
78
John F. Horty
Introduction
111
7
Background
111
3
Overview
114
2
Basic concepts
116
2
Theories of defeasible inheritance
118
16
Defeasible inheritability
118
4
Constructing extensions
122
12
Theories of mixed inheritance
134
16
Strict inheritability
135
3
Mixed inheritability
138
7
Constructing extensions
145
5
Discussion
150
39
Decoupling and stability
150
4
Varieties of preemption
154
8
A fixed-point approach to sceptical inheritance
162
4
Translational theories and meaning holism
166
7
Implementational concerns
173
3
A Proofs of selected theorems
176
13
Default Logic
189
28
David Poole
Logic and monotonicity
189
1
Reiter's logic for default reasoning
190
3
Examples
193
6
Normal defaults
193
2
Nonnormal defaults
195
2
Equality
197
1
Skolemization
198
1
Semantics
199
5
Fixed points
199
1
Stable model semantics
200
1
Maximal models
200
1
Epistemic semantics
201
1
Sceptical prediction
202
2
Relationship to other formalisms
204
1
Autoepistemic logic
204
1
Circumscription
204
1
Implementation
205
2
Forward-chaining default prover
205
1
Backward-chaining default prover
205
1
Sceptical prediction
206
1
When does an extension exist?
207
1
Complexity
208
1
Empirical investigations
209
1
Applications
209
1
Variations
210
7
Autoepistemic Logic
217
80
Kurt Konolige
Introduction
218
1
Belief-set semantics and fixed points
219
10
Language and notation
219
1
Extensions
220
2
Multiplicity
222
3
Stable sets
225
2
Fixed-points and modal systems
227
2
Further topics
229
10
Normal forms
229
3
Groundedness
232
4
Possible-worlds semantics
236
1
Equality
237
2
Extending AE logic
239
17
Assumption variants
240
5
Incoherent theories
245
3
Hierarchic AE logic
248
3
Metatheory
251
3
Knowledge and minimization
254
2
Quantifying-in
256
14
Belief-set semantics
257
4
Possible-worlds semantics
261
2
Knowing who
263
2
Representational issues
265
5
Correspondences
270
13
Translations
271
1
Default logic
271
5
Circumscription
276
2
Truth maintenance systems
278
3
Logic programming
281
2
Proof theory
283
14
Model construction
284
1
Reduced extension bases
284
1
Tableaux
285
1
Translation to TMS
286
2
Hilbert systems
288
9
Circumscription
297
56
Vladimir Lifschitz
Introduction
298
2
Definition and examples
300
9
The basic case
300
2
Propositional circumscription
302
1
Varying constants
303
2
Many-sorted and higher-order circumscription
305
1
Models of circumscription
306
1
Circumscriptive theories
307
2
Rules for computing circumscription
309
13
Predicate completion
309
3
Elimination of varied constants
312
3
Positive and negative formulae
315
3
Confirming conjectures about circumscription
318
2
Definite formulae
320
2
Circumscriptive theories of inheritance
322
6
Three examples
322
2
Priorities
324
3
Unresolved conflicts in inheritance hierarchies
327
1
Circumscriptive theories of action
328
6
Situations and states
328
3
Actions
331
2
Preconditions
333
1
Well-foundedness
334
6
Definition and examples
334
1
Syntactic sufficient conditions
335
2
Satisfiability of circumscription
337
1
Limitations of circumscription
338
1
A characterization of minimal models
339
1
Circumscribing several predicates
340
6
Parallel circumscription
340
3
Prioritized circumscription
343
3
Bibliographical and historical remarks
346
7
Defeasible Logic
353
44
Donald Nute
Introduction
353
5
Nute's defeasible logics
358
9
The monotonic kernel of defeasible logic
358
3
Superiority relations on rules
361
2
Specificity based systems
363
4
Delgrande and conditional logic
367
1
Delgrande and conditional logic
367
6
Proof theory for familiar conditional logics
367
2
Semantics for conditional logics
369
3
Delgrande's weak conditional logic N
372
1
Geffner--Pearl and probabilistic entailment
373
5
The probabilistic core and two irrelevance rules
373
2
Consequences of the systems P, GP, and G
375
3
Loui and more evidence
378
4
Loui's formal system
378
1
Comparing arguments
379
3
Pollock's theory of warrant
382
6
Defeasible reasoning as an iterative process
382
3
Comparison with other systems
385
3
Other defeasible formalisms
388
9
Uncertainty Logics
397
42
Henry E. Kyburg, Jr.
Introduction
397
4
Subjectivism
401
5
Nilsson's probabilistic logic
406
4
Belief functions
410
2
Possible worlds
412
2
Representing statistical facts
414
2
Combining measures and probabilities
416
4
Evidential probability
420
3
Updating
423
1
Inference
424
6
Conclusion
430
9
Possibilistic Logic
439
64
D. Dubois
J. Lang
H. Parade
Introduction
439
4
Possibility theory
443
6
Possibilistic logic: the case of necessity-valued formulae
449
23
Language
450
1
A semantics coping with partial inconsistency
451
3
Partial inconsistency
454
2
Fuzzy sets of interpretations and best models
456
2
Deduction under partial inconsistency
458
2
A formal system for necessity-valued logic
460
1
Qualitative possibilistic logic and conditional logic
461
1
Automated deduction
461
5
Nonmonotonic aspects
466
5
Belief revision and possibilistic logic
471
1
Generalizations of possibilistic logic
472
15
Possibilistic logic
473
9
Variable valuations
482
1
L-possibilistic logics
483
2
Weighted logics
485
1
Possibilistic logic with vague predictes
486
1
Some applications
487
6
Possibilistic management of assumptions
487
2
Discrete optimization
489
2
Logic programming
491
2
Conclusion
493
10
A Appendix
503
12
A.1 Proofs of results from Section 3
504
6
A.2 Proofs of results from Section 4
510
5
Index
515