Uncertain Inference

, by Henry E. Kyburg, Jr , Choh Man Teng

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ISBN: 9780521800648 | 0521800641
Cover: Hardcover
Copyright: 8/6/2001

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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.

Preface

Historical Background

(20)

Introduction

(1)

Inference

(5)

Roots in the Past

(1)

Francis Bacon

(3)

The Development of Probability

(3)

John Stuart Mill

(4)

G. H. von Wright

(2)

Bibliographical Notes

(1)

Exercises

(2)

Bibliography

(1)

First Order Logic

(21)

Introduction

(3)

Syntax

(4)

Semantics

(2)

W. V. O. Quine's Mathematical Logic

(3)

Arguments from Premises

(1)

Limitations

(5)

Summary

(1)

Bibliographical Notes

(1)

Exercises

(3)

Bibliography

(1)

The Probability Calculus

(26)

Introduction

(2)

Elementary Probability

(6)

Combinations and Permutations

(3)

The Probability Calculus

(2)

Elementary Theorems

(1)

Conditional Probability

(4)

The Axiom of Conditional Probability

(2)

Bayes' Theorem

(1)

Probability Distributions

(7)

Frequency Functions and Distribution Functions

(4)

Properties of Distributions

(2)

Sampling Distributions

(1)

Useful Distributions

(2)

Summary

(1)

Bibliographical Notes

(1)

Exercises

(3)

Bibliography

(1)

Interpretations of Probability

(30)

Introduction

(1)

The Classical View

(3)

Empirical Interpretations of Probability

(9)

The Limiting Frequency Interpretation

(6)

The Propensity Interpretation

(2)

Logical Interpretations of Probability

(7)

Subjective Interpretations of Probability

(6)

Dutch Book

(2)

Conditionalization

(4)

Summary

(2)

Bibliographical Notes

(1)

Exercises

(3)

Bibliography

(2)

Nonstandard Measures of Support

(19)

Support

(1)

Karl Popper

(4)

Corroboration

100

(2)

Levi's Criticism

102

(1)

Other Measures

103

(1)

Dempster--Shafer Belief Functions

104

(9)

Belief Functions and Mass Functions

105

(1)

Reduction to Sets of Probabilities

106

(2)

Combining Evidence

108

(2)

Special Cases

110

(1)

Assessment of Belief Functions

111

(2)

Sets of Probability Functions

113

(1)

Summary

114

(1)

Bibliographical Notes

114

(1)

Exercises

115

(2)

Bibliography

116

(1)

Nonmonotonic Reasoning

117

(35)

Introduction

117

(1)

Logic and (Non)monotonicity

117

(4)

Default Logic

121

(13)

Preliminaries

121

(2)

Transformation of Open Default Theories

123

(1)

Extensions

124

(2)

Need for a Fixed Point

126

(1)

Number of Extensions

127

(1)

Representation

128

(3)

Variants of Default Logic

131

(3)

Autoepistemic Logic

134

(9)

Modal Logic

134

(2)

Autoepistemic Reasoning vs Default Reasoning

136

(2)

Stable Expansions

138

(2)

Alternative Fixed-Point Formulation

140

(2)

Groundedness

142

(1)

Circumscription

143

(3)

Unresolved Issues

146

(2)

``Intuition'': Basis of Defaults

146

(1)

Computational Complexity

147

(1)

Multiple Extensions

147

(1)

Summary

148

(1)

Bibliographical Notes

148

(1)

Exercises

149

(3)

Bibliography

150

(2)

Theory Replacement

152

(23)

Introduction

152

(1)

Theory Change

153

(3)

Expansion

153

(1)

Contraction

154

(1)

Revision

155

(1)

Rationality Considerations

156

(2)

The AGM Postulates

158

(5)

Expansion

158

(1)

Contraction

159

(2)

Revision

161

(2)

Connections

163

(1)

Selecting a Contraction Function

164

(2)

Epistemic Entrenchment

166

(2)

Must It Be?

168

(3)

Belief Bases

168

(1)

Updates

169

(1)

Rationality Revisited

170

(1)

Iterated Change

171

(1)

Summary

171

(1)

Bibliographical Notes

172

(1)

Exercises

172

(3)

Bibliography

173

(2)

Statistical Inference

175

(25)

Introduction

175

(3)

Classical Statistics

178

(14)

Significance Tests

179

(3)

Hypothesis Testing

182

(4)

Confidence Intervals

186

(6)

Bayesian Statistics

192

(3)

Summary

195

(2)

Bibliographical Notes

197

(1)

Exercises

197

(3)

Bibliography

198

(2)

Evidential Probability

200

(30)

Introduction

200

(1)

Background Issues and Assumptions

201

(2)

The Syntax of Statistical Knowledge

203

(2)

Reference Classes and Target Classes

205

(4)

Reference Formulas

205

(3)

Target Formulas

208

(1)

Prima Facie Support

209

(3)

Indefinite Probabilities

210

(1)

Definite Probabilities

210

(2)

Sharpening

212

(7)

Precision

213

(1)

Specificity

213

(3)

Richness

216

(1)

Sharpens

217

(2)

Partial Proof

219

(1)

Extended Example

220

(5)

A Useful Algorithm

225

(1)

Relations to Other Interpretations

225

(1)

Summary

226

(1)

Bibliographical Notes

227

(1)

Exercises

227

(3)

Bibliography

228

(2)

Semantics

230

(17)

Introduction

230

(2)

Models and Truth

232

(3)

Model Ratios

235

(1)

Relevant Models

236

(4)

Partial Validity

240

(2)

Remarks

242

(2)

Summary

244

(1)

Bibliographical Notes

245

(1)

Exercises

245

(2)

Bibliography

245

(2)

Applications

247

(23)

Introduction

247

(1)

Elementary Results

248

(6)

Inference from Samples

254

(5)

Example

259

(2)

Statistical Induction

261

(1)

Bayesian Induction

262

(2)

Sequences of Draws

264

(2)

Summary

266

(1)

Bibliographical Notes

267

(1)

Exercises

268

(2)

Bibliography

268

(2)

Scientific Inference

270

(21)

Introduction

270

(4)

Objectivity

270

(2)

Evidential and Practical Certainty

272

(1)

Statistical Inference

273

(1)

Demonstrative Induction

274

(1)

Direct Measurement

275

(5)

Indirect Measurement

280

(5)

Theory, Language, and Error

285

(1)

Summary

286

(1)

Bibliographical Notes

287

(1)

Measurement

287

(1)

Theories

287

(1)

Datamining

287

(1)

Exercises

288

(3)

Bibliography

288

(3)

Names Index

291

(2)

Index

293

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Uncertain Inference

Summary

Table of Contents

Supplemental Materials