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Uncertain Inference - Henry E. Kyburg, Jr.

Hardcover Published: 4th March 2015
ISBN: 9780521800648
Number Of Pages: 312

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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. 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.

"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

Prefacep. xi
Historical Backgroundp. 1
Introductionp. 1
Inferencep. 1
Roots in the Pastp. 6
Francis Baconp. 7
The Development of Probabilityp. 10
John Stuart Millp. 13
G. H. von Wrightp. 17
Bibliographical Notesp. 19
Exercisesp. 19
Bibliographyp. 20
First Order Logicp. 21
Introductionp. 21
Syntaxp. 24
Semanticsp. 28
W. V. O. Quine's Mathematical Logicp. 30
Arguments from Premisesp. 33
Limitationsp. 34
Summaryp. 39
Bibliographical Notesp. 39
Exercisesp. 39
Bibliographyp. 41
The Probability Calculusp. 42
Introductionp. 42
Elementary Probabilityp. 44
Combinations and Permutationsp. 44
The Probability Calculusp. 47
Elementary Theoremsp. 49
Conditional Probabilityp. 50
The Axiom of Conditional Probabilityp. 51
Bayes' Theoremp. 53
Probability Distributionsp. 54
Frequency Functions and Distribution Functionsp. 55
Properties of Distributionsp. 59
Sampling Distributionsp. 61
Useful Distributionsp. 62
Summaryp. 64
Bibliographical Notesp. 65
Exercisesp. 65
Bibliographyp. 67
Interpretations of Probabilityp. 68
Introductionp. 68
The Classical Viewp. 68
Empirical Interpretations of Probabilityp. 71
The Limiting Frequency Interpretationp. 72
The Propensity Interpretationp. 78
Logical Interpretations of Probabilityp. 80
Subjective Interpretations of Probabilityp. 87
Dutch Bookp. 87
Conditionalizationp. 89
Summaryp. 93
Bibliographical Notesp. 95
Exercisesp. 95
Bibliographyp. 96
Nonstandard Measures of Supportp. 98
Supportp. 98
Karl Popperp. 99
Corroborationp. 100
Levi's Criticismp. 102
Other Measuresp. 103
Dempster-Shafer Belief Functionsp. 104
Belief Functions and Mass Functionsp. 105
Reduction to Sets of Probabilitiesp. 106
Combining Evidencep. 108
Special Casesp. 110
Assessment of Belief Functionsp. 111
Sets of Probability Functionsp. 113
Summaryp. 114
Bibliographical Notesp. 114
Exercisesp. 115
Bibliographyp. 116
Nonmonotonic Reasoningp. 117
Introductionp. 117
Logic and (Non)monotonicityp. 117
Default Logicp. 121
Preliminariesp. 121
Transformation of Open Default Theoriesp. 123
Extensionsp. 124
Need for a Fixed Pointp. 126
Number of Extensionsp. 127
Representationp. 128
Variants of Default Logicp. 131
Autoepistemic Logicp. 134
Modal Logicp. 134
Autoepistemic Reasoning vs Default Reasoningp. 136
Stable Expansionsp. 138
Alternative Fixed-Point Formulationp. 140
Groundednessp. 142
Circumscriptionp. 143
Unresolved Issuesp. 146
"Intuition": Basis of Defaultsp. 146
Computational Complexityp. 147
Multiple Extensionsp. 147
Summaryp. 148
Bibliographical Notesp. 148
Exercisesp. 149
Bibliographyp. 150
Theory Replacementp. 152
Introductionp. 152
Theory Changep. 153
Expansionp. 153
Contractionp. 154
Revisionp. 155
Rationality Considerationsp. 156
The AGM Postulatesp. 158
Expansionp. 158
Contractionp. 159
Revisionp. 161
Connectionsp. 163
Selecting a Contraction Functionp. 164
Epistemic Entrenchmentp. 166
Must It Be?p. 168
Belief Basesp. 168
Updatesp. 169
Rationality Revisitedp. 170
Iterated Changep. 171
Summaryp. 171
Bibliographical Notesp. 172
Exercisesp. 172
Bibliographyp. 173
Statistical Inferencep. 175
Introductionp. 175
Classical Statisticsp. 178
Significance Testsp. 179
Hypothesis Testingp. 182
Confidence Intervalsp. 186
Bayesian Statisticsp. 192
Summaryp. 195
Bibliographical Notesp. 197
Exercisesp. 197
Bibliographyp. 198
Evidential Probabilityp. 200
Introductionp. 200
Background Issues and Assumptionsp. 201
The Syntax of Statistical Knowledgep. 203
Reference Classes and Target Classesp. 205
Reference Formulasp. 205
Target Formulasp. 208
Prima Facie Supportp. 209
Indefinite Probabilitiesp. 210
Definite Probabilitiesp. 210
Sharpeningp. 212
Precisionp. 213
Specificityp. 213
Richnessp. 216
Sharpensp. 217
Partial Proofp. 219
Extended Examplep. 220
A Useful Algorithmp. 225
Relations to Other Interpretationsp. 225
Summaryp. 226
Bibliographical Notesp. 227
Exercisesp. 227
Bibliographyp. 228
Semanticsp. 230
Introductionp. 230
Models and Truthp. 232
Model Ratiosp. 235
Relevant Modelsp. 236
Partial Validityp. 240
Remarksp. 242
Summaryp. 244
Bibliographical Notesp. 245
Exercisesp. 245
Bibliographyp. 245
Applicationsp. 247
Introductionp. 247
Elementary Resultsp. 248
Inference from Samplesp. 254
Examplep. 259
Statistical Inductionp. 261
Bayesian Inductionp. 262
Sequences of Drawsp. 264
Summaryp. 266
Bibliographical Notesp. 267
Exercisesp. 268
Bibliographyp. 268
Scientific Inferencep. 270
Introductionp. 270
Objectivityp. 270
Evidential and Practical Certaintyp. 272
Statistical Inferencep. 273
Demonstrative Inductionp. 274
Direct Measurementp. 275
Indirect Measurementp. 280
Theory, Language, and Errorp. 285
Summaryp. 286
Bibliographical Notesp. 287
Measurementp. 287
Theoriesp. 287
Dataminingp. 287
Exercisesp. 288
Bibliographyp. 288
Names Indexp. 291
Indexp. 293
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521800648
ISBN-10: 0521800641
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 312
Published: 4th March 2015
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 25.3 x 17.7  x 1.9
Weight (kg): 0.7