Coping with uncertainty is a necessary part of ordinary life and is crucial to an understanding of how the mind works. It is a vital element in developing artificial intelligence that will not be undermined by its own rigidities. There have been many approaches to the problem of uncertain inference, ranging from probability to inductive logic to nonmonotonic logic. This book seeks to provide a clear exposition of these approaches within a unified framework.
Author(s): Henry E. Kyburg, Jr., Choh Man Teng
Publisher: Cambridge University Press
Year: 2001
Language: English
Pages: 312
Tags: Информатика и вычислительная техника;Искусственный интеллект;
Cover......Page 1
Abstract......Page 3
Title Page......Page 5
Contents......Page 7
Preface......Page 13
1.2 Inference......Page 15
1.3 Roots in the Past......Page 20
1.4 Francis Bacon......Page 21
1.5 The Development of Probability......Page 24
1.6 John Stuart Mill......Page 27
1.7 G. H. von Wright......Page 31
1.9 Exercises......Page 33
Bibliography......Page 34
2.1 Introduction......Page 35
2.2 Syntax......Page 38
2.3 Semantics......Page 42
2.4 W. V. O. Quine’s Mathematical Logic......Page 44
2.5 Arguments from Premises......Page 47
2.6 Limitations......Page 48
2.9 Exercises......Page 53
Bibliography......Page 55
3.1 Introduction......Page 56
3.2.1 Combinations and Permutations......Page 58
3.2.2 The Probability Calculus......Page 61
3.2.3 Elementary Theorems......Page 63
3.3 Conditional Probability......Page 64
3.3.1 The Axiom of Conditional Probability......Page 65
3.3.2 Bayes’ Theorem......Page 67
3.4 Probability Distributions......Page 68
3.4.1 Frequency Functions and Distribution Functions......Page 69
3.4.2 Properties of Distributions......Page 73
3.5 Sampling Distributions......Page 75
3.6 Useful Distributions......Page 76
3.7 Summary......Page 78
3.9 Exercises......Page 79
Bibliography......Page 81
4.2 The Classical View......Page 82
4.3 Empirical Interpretations of Probability......Page 85
4.3.1 The Limiting Frequency Interpretation......Page 86
4.3.2 The Propensity Interpretation......Page 92
4.4 Logical Interpretations of Probability......Page 94
4.5.1 Dutch Book......Page 101
4.5.2 Conditionalization......Page 103
4.6 Summary......Page 107
4.8 Exercises......Page 109
Bibliography......Page 110
5.1 Support......Page 112
5.2 Karl Popper......Page 113
5.2.1 Corroboration......Page 114
5.2.2 Levi’s Criticism......Page 116
5.3 Other Measures......Page 117
5.4 Dempster–Shafer Belief Functions......Page 118
5.4.1 Belief Functions and Mass Functions......Page 119
5.4.2 Reduction to Sets of Probabilities......Page 120
5.4.3 Combining Evidence......Page 122
5.4.4 Special Cases......Page 124
5.4.5 Assessment of Belief Functions......Page 125
5.5 Sets of Probability Functions......Page 127
5.7 Bibliographical Notes......Page 128
5.8 Exercises......Page 129
Bibliography......Page 130
6.2 Logic and (Non)monotonicity......Page 131
6.3.1 Preliminaries......Page 135
6.3.2 Transformation of Open Default Theories......Page 137
6.3.3 Extensions......Page 138
6.3.4 Need for a Fixed Point......Page 140
6.3.5 Number of Extensions......Page 141
6.3.6 Representation......Page 142
6.3.7 Variants of Default Logic......Page 145
6.4.1 Modal Logic......Page 148
6.4.2 Autoepistemic Reasoning vs Default Reasoning......Page 150
6.4.3 Stable Expansions......Page 152
6.4.4 Alternative Fixed-Point Formulation......Page 154
6.4.5 Groundedness......Page 156
6.5 Circumscription......Page 157
6.6.1 “Intuition”: Basis of Defaults......Page 160
6.6.3 Multiple Extensions......Page 161
6.8 Bibliographical Notes......Page 162
6.9 Exercises......Page 163
Bibliography......Page 164
7.1 Introduction......Page 166
7.2.1 Expansion......Page 167
7.2.2 Contraction......Page 168
7.2.3 Revision......Page 169
7.3 Rationality Considerations......Page 170
7.4.1 Expansion......Page 172
7.4.2 Contraction......Page 173
7.4.3 Revision......Page 175
7.5 Connections......Page 177
7.6 Selecting a Contraction Function......Page 178
7.7 Epistemic Entrenchment......Page 180
7.8.1 Belief Bases......Page 182
7.8.2 Updates......Page 183
7.8.3 Rationality Revisited......Page 184
7.9 Summary......Page 185
7.11 Exercises......Page 186
Bibliography......Page 187
8.1 Introduction......Page 189
8.2 Classical Statistics......Page 192
8.2.1 Significance Tests......Page 193
8.2.2 Hypothesis Testing......Page 196
8.2.3 Confidence Intervals......Page 200
8.3 Bayesian Statistics......Page 206
8.4 Summary......Page 209
8.6 Exercises......Page 211
Bibliography......Page 212
9.1 Introduction......Page 214
9.2 Background Issues and Assumptions......Page 215
9.3 The Syntax of Statistical Knowledge......Page 217
9.4.1 Reference Formulas......Page 219
9.4.2 Target Formulas......Page 222
9.5 Prima Facie Support......Page 223
9.5.2 Definite Probabilities......Page 224
9.6 Sharpening......Page 226
9.6.2 Specificity......Page 227
9.6.3 Richness......Page 230
9.6.4 Sharpens......Page 231
9.7 Partial Proof......Page 233
9.8 Extended Example......Page 234
9.10 Relations to Other Interpretations......Page 239
9.11 Summary......Page 240
9.13 Exercises......Page 241
Bibliography......Page 242
10.1 Introduction......Page 244
10.2 Models and Truth......Page 246
10.3 Model Ratios......Page 249
10.4 Relevant Models......Page 250
10.5 Partial Validity......Page 254
10.6 Remarks......Page 256
10.7 Summary......Page 258
Bibliography......Page 259
11.1 Introduction......Page 261
11.2 Elementary Results......Page 262
11.3 Inference from Samples......Page 268
11.4 Example......Page 273
11.5 Statistical Induction......Page 275
11.6 Bayesian Induction......Page 276
11.7 Sequences of Draws......Page 278
11.8 Summary......Page 280
11.9 Bibliographical Notes......Page 281
Bibliography......Page 282
12.1.1 Objectivity......Page 284
12.1.2 Evidential and Practical Certainty......Page 286
12.1.3 Statistical Inference......Page 287
12.2 Demonstrative Induction......Page 288
12.3 Direct Measurement......Page 289
12.4 Indirect Measurement......Page 294
12.5 Theory, Language, and Error......Page 299
12.6 Summary......Page 300
12.7.3 Datamining......Page 301
Bibliography......Page 302
Names Index......Page 305
Index......Page 307
