Uncertain Inference

By: Jr Henry E. Kyburg, Choh Man Teng

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Hardcover | 25 October 2001

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312 Pages

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25.4 x 17.78 x 1.91

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Coping with uncertainty is a necessary part of ordinary life and is crucial to an understanding of how the mind works. For example, 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. Thisbook seeks to provide a clear exposition of these approaches within a unified framework. The principal market for the book will be students and professionals in philosophy, computer science, and AI. Among the special features of the book are a chapter on evidential probability, which has not received a basic exposition before; chapters on nonmonotonic reasoning and theory replacement, matters rarely addressed in standard philosophical texts; and chapters on Mill's methods and statistical inference that cover material sorely lacking in the usual treatments of AI and computer science.

Industry Reviews

"Overall this book is one of the most thorough and objective treatments of inductive reasoning that I have encountered. It is clearly written with well chosen examples and both the scope and depth of the material covered is impressive...an excellent postgraduate textbook." Mathematical Reviews

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Non-Fiction Mathematics Mathematical Foundation Mathematical Logic Reference, Information & Interdisciplinary Subjects Research & Information Information theory Probability & Statistics Science Science in General Philosophy of Science Philosophy

Philosophy & Logic Computing & I.T.Computer Science Artificial Intelligence

Preface	p. xi
Historical Background	p. 1
Introduction	p. 1
Inference	p. 1
Roots in the Past	p. 6
Francis Bacon	p. 7
The Development of Probability	p. 10
John Stuart Mill	p. 13
G. H. von Wright	p. 17
Bibliographical Notes	p. 19
Exercises	p. 19
Bibliography	p. 20
First Order Logic	p. 21
Introduction	p. 21
Syntax	p. 24
Semantics	p. 28
W. V. O. Quine's Mathematical Logic	p. 30
Arguments from Premises	p. 33
Limitations	p. 34
Summary	p. 39
Bibliographical Notes	p. 39
Exercises	p. 39
Bibliography	p. 41
The Probability Calculus	p. 42
Introduction	p. 42
Elementary Probability	p. 44
Combinations and Permutations	p. 44
The Probability Calculus	p. 47
Elementary Theorems	p. 49
Conditional Probability	p. 50
The Axiom of Conditional Probability	p. 51
Bayes' Theorem	p. 53
Probability Distributions	p. 54
Frequency Functions and Distribution Functions	p. 55
Properties of Distributions	p. 59
Sampling Distributions	p. 61
Useful Distributions	p. 62
Summary	p. 64
Bibliographical Notes	p. 65
Exercises	p. 65
Bibliography	p. 67
Interpretations of Probability	p. 68
Introduction	p. 68
The Classical View	p. 68
Empirical Interpretations of Probability	p. 71
The Limiting Frequency Interpretation	p. 72
The Propensity Interpretation	p. 78
Logical Interpretations of Probability	p. 80
Subjective Interpretations of Probability	p. 87
Dutch Book	p. 87
Conditionalization	p. 89
Summary	p. 93
Bibliographical Notes	p. 95
Exercises	p. 95
Bibliography	p. 96
Nonstandard Measures of Support	p. 98
Support	p. 98
Karl Popper	p. 99
Corroboration	p. 100
Levi's Criticism	p. 102
Other Measures	p. 103
Dempster-Shafer Belief Functions	p. 104
Belief Functions and Mass Functions	p. 105
Reduction to Sets of Probabilities	p. 106
Combining Evidence	p. 108
Special Cases	p. 110
Assessment of Belief Functions	p. 111
Sets of Probability Functions	p. 113
Summary	p. 114
Bibliographical Notes	p. 114
Exercises	p. 115
Bibliography	p. 116
Nonmonotonic Reasoning	p. 117
Introduction	p. 117
Logic and (Non)monotonicity	p. 117
Default Logic	p. 121
Preliminaries	p. 121
Transformation of Open Default Theories	p. 123
Extensions	p. 124
Need for a Fixed Point	p. 126
Number of Extensions	p. 127
Representation	p. 128
Variants of Default Logic	p. 131
Autoepistemic Logic	p. 134
Modal Logic	p. 134
Autoepistemic Reasoning vs Default Reasoning	p. 136
Stable Expansions	p. 138
Alternative Fixed-Point Formulation	p. 140
Groundedness	p. 142
Circumscription	p. 143
Unresolved Issues	p. 146
"Intuition": Basis of Defaults	p. 146
Computational Complexity	p. 147
Multiple Extensions	p. 147
Summary	p. 148
Bibliographical Notes	p. 148
Exercises	p. 149
Bibliography	p. 150
Theory Replacement	p. 152
Introduction	p. 152
Theory Change	p. 153
Expansion	p. 153
Contraction	p. 154
Revision	p. 155
Rationality Considerations	p. 156
The AGM Postulates	p. 158
Expansion	p. 158
Contraction	p. 159
Revision	p. 161
Connections	p. 163
Selecting a Contraction Function	p. 164
Epistemic Entrenchment	p. 166
Must It Be?	p. 168
Belief Bases	p. 168
Updates	p. 169
Rationality Revisited	p. 170
Iterated Change	p. 171
Summary	p. 171
Bibliographical Notes	p. 172
Exercises	p. 172
Bibliography	p. 173
Statistical Inference	p. 175
Introduction	p. 175
Classical Statistics	p. 178
Significance Tests	p. 179
Hypothesis Testing	p. 182
Confidence Intervals	p. 186
Bayesian Statistics	p. 192
Summary	p. 195
Bibliographical Notes	p. 197
Exercises	p. 197
Bibliography	p. 198
Evidential Probability	p. 200
Introduction	p. 200
Background Issues and Assumptions	p. 201
The Syntax of Statistical Knowledge	p. 203
Reference Classes and Target Classes	p. 205
Reference Formulas	p. 205
Target Formulas	p. 208
Prima Facie Support	p. 209
Indefinite Probabilities	p. 210
Definite Probabilities	p. 210
Sharpening	p. 212
Precision	p. 213
Specificity	p. 213
Richness	p. 216
Sharpens	p. 217
Partial Proof	p. 219
Extended Example	p. 220
A Useful Algorithm	p. 225
Relations to Other Interpretations	p. 225
Summary	p. 226
Bibliographical Notes	p. 227
Exercises	p. 227
Bibliography	p. 228
Semantics	p. 230
Introduction	p. 230
Models and Truth	p. 232
Model Ratios	p. 235
Relevant Models	p. 236
Partial Validity	p. 240
Remarks	p. 242
Summary	p. 244
Bibliographical Notes	p. 245
Exercises	p. 245
Bibliography	p. 245
Applications	p. 247
Introduction	p. 247
Elementary Results	p. 248
Inference from Samples	p. 254
Example	p. 259
Statistical Induction	p. 261
Bayesian Induction	p. 262
Sequences of Draws	p. 264
Summary	p. 266
Bibliographical Notes	p. 267
Exercises	p. 268
Bibliography	p. 268
Scientific Inference	p. 270
Introduction	p. 270
Objectivity	p. 270
Evidential and Practical Certainty	p. 272
Statistical Inference	p. 273
Demonstrative Induction	p. 274
Direct Measurement	p. 275
Indirect Measurement	p. 280
Theory, Language, and Error	p. 285
Summary	p. 286
Bibliographical Notes	p. 287
Measurement	p. 287
Theories	p. 287
Datamining	p. 287
Exercises	p. 288
Bibliography	p. 288
Names Index	p. 291
Index	p. 293
Table of Contents provided by Syndetics. All Rights Reserved.

Uncertain Inference

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Hardcover

Industry Reviews

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