From preface: Non-monotonic reasoning can be loosely described as the process of drawing conclusions which may be invalidated by new information. Owing to its close relationship to human common-sense reasoning, non-monotonic inference has become one of the major research topics in the field of artificial intelligence (AI).
I have attempted to achieve two goals in writing this book. One was to explain what non-monotonic reasoning is and how it has been approached in the AI research. The other was to provide a detailed study of the most influential non-monotonic logics. The book is primarily addressed to students and research workers in AI (and related disciplines), but should also be useful to practitioners involved in expert and intelligent knowledge-based systems.
Author(s): Witold Lukaszewicz
Series: Ellis Horwood series in artificial intelligence
Publisher: Ellis Horwood
Year: 1990
Language: English
Commentary: Scanned, DjVu'ed, OCR'ed, TOC by Envoy
Pages: 331
Cover ......Page 1
Table of contents ......Page 7
Preface ......Page 11
Acknowledgements ......Page 13
Notation ......Page 15
List of non-monotonic logics discussed in the book ......Page 21
1.1 Basic notions ......Page 23
1.2 Classical propositional logic ......Page 28
1.2.1 Language of propositional logic ......Page 29
1.2.2. Semantics of propositional logic ......Page 30
1.2.3 Propositional theories ......Page 33
1.2.4 Propositional logic as a deduction system ......Page 35
1.3.1 Language of first-order logic ......Page 38
1.3.2 Semantics of first-order logic ......Page 40
1.3.3 First-order theories ......Page 45
1.3.4 First-order logic as a deduction system ......Page 47
1.3.5 Many-sorted first-order logic ......Page 48
1.4 Resolution method ......Page 51
1.4.1 Clausal form ......Page 52
1.4.2 Resolution rule ......Page 55
1.4.3 Linear resolution ......Page 60
1.5 Classical second-order logic ......Page 62
1.5.1 Language of second-order logic ......Page 63
1.5.2 Semantics of second-order logic ......Page 64
1.5.4 Deduction systems for second-order logic ......Page 66
1.5.5 Predicate and function expressions ......Page 67
1.6.1 Modal propositional logic ......Page 71
1.6.2 Modal first-order logic ......Page 75
2.1 Non-monotonic reasoning ......Page 79
2.2 Non-monotonic inference and reasoning about action ......Page 84
2.3 Typology of non-monotonic reasoning ......Page 86
3.1.1 MICRO-PLANNER ......Page 90
3.1.2 Network- and frame-based systems ......Page 92
3.1.3 Systems employing meta-level reasoning facilities ......Page 96
3.1.4 Truth Maintenance systems ......Page 99
3.2.1 Sandewall’s formalism ......Page 104
3.2.3 Default logic ......Page 105
3.2.4 Circumscription ......Page 106
3.2.6 Poole’s approach to non-monotonic reasoning ......Page 107
3.2.7 Model-theoretic approach to non-monotonic reasoning ......Page 108
3.3 Objections to non-monotonic formalisms ......Page 109
4 Modal non-monotonic logics ......Page 113
4.1 Modal non-monotonic logic of McDermott and Doyle ......Page 114
4.2 Modal non-monotonic logics of McDermott ......Page 118
4.3.1 Preliminaries ......Page 124
4.3.2 Semantic considerations ......Page 125
4.3.3 Syntactic characterization of AE extensions ......Page 128
4.3.4 Possible-world semantics for autoepistemic logic ......Page 135
4.3.5 Reduction theorem ......Page 141
4.3.6 Minimal, strongly grounded and superstrongly grounded AE extensions ......Page 143
4.3.7 A comparison of autoepistemic logic to non-monotonic logics of McDermott and Doyle ......Page 147
4.3.8 Conclusions ......Page 150
4.4.1 Intuitionistic basis for modal non-monotonic logic ......Page 151
4.4.2 3-valued basis for modal non-monotonic logic ......Page 156
5 Default logic ......Page 161
5.1 Preliminaries ......Page 162
5.2 Open defaults and their instances ......Page 166
5.3 Closed default theories ......Page 170
5.4 Normal default theories ......Page 175
5.5 Representational issues ......Page 181
5.6 Semi-normal default theories ......Page 186
5.7 Semantic characterization of extensions ......Page 189
5.8 Proof theory for closed normal default theories ......Page 194
5.9 A comparison between default logic and autoepistemic logic ......Page 201
5.10 Alternative formalization of default logic ......Page 204
5.11 Basic properties of the new formalization ......Page 207
5.12 Semantic characterization of m-extensions ......Page 221
5.13 Proof theory for alternative default logic ......Page 226
6.1 Introduction ......Page 228
6.2 Abnormality formalism ......Page 230
6.3.1 Preliminaries ......Page 232
6.3.2 Semantics for predicate circumscription ......Page 235
6.3.3 Consistency of predicate circumscription ......Page 240
6.3.4 Expressive power of predicate circumscription ......Page 241
6.4 Formula circumscription ......Page 243
6.5.1 Preliminaries ......Page 247
6.5.2 Satisfiability of second-order circumscription ......Page 250
6.5.3 Reducing second-order circumscription to first-order logic ......Page 251
6.5.4 Expressive power of second-order circumscription ......Page 254
6.5.5 Prioritized second-order circumscription ......Page 256
6.6 Non-recursive circumscription ......Page 262
6.7 Domain circumscription ......Page 264
6.8.1 The basic case ......Page 269
6.8.2 Minimizing several predicates ......Page 271
6.8.3 General pointwise circumscription ......Page 273
6.9 Conclusions ......Page 279
7.1 Introduction ......Page 283
7.2 Naive CWA ......Page 284
7.3 Generalized CWA ......Page 290
7.4 Careful CWA ......Page 294
7.5 Extended CWA ......Page 299
7.6 Theory completion ......Page 302
Bibliography ......Page 311
Index ......Page 321
Back cover ......Page 331
