Uncertain Inference

by Henry E. Kyburg, Jr , Choh Man Teng

• ISBN13: 9780521800648
• ISBN10: 0521800641
• Edition: 1st
• Format: Hardcover
• Copyright: 2001-08-06
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Preface	xi
Historical Background	1	(20)
Introduction	1	(1)
Inference	1	(5)
Roots in the Past	6	(1)
Francis Bacon	7	(3)
The Development of Probability	10	(3)
John Stuart Mill	13	(4)
G. H. von Wright	17	(2)
Bibliographical Notes	19	(1)
Exercises	19	(2)
Bibliography	20	(1)
First Order Logic	21	(21)
Introduction	21	(3)
Syntax	24	(4)
Semantics	28	(2)
W. V. O. Quine's Mathematical Logic	30	(3)
Arguments from Premises	33	(1)
Limitations	34	(5)
Summary	39	(1)
Bibliographical Notes	39	(1)
Exercises	39	(3)
Bibliography	41	(1)
The Probability Calculus	42	(26)
Introduction	42	(2)
Elementary Probability	44	(6)
Combinations and Permutations	44	(3)
The Probability Calculus	47	(2)
Elementary Theorems	49	(1)
Conditional Probability	50	(4)
The Axiom of Conditional Probability	51	(2)
Bayes' Theorem	53	(1)
Probability Distributions	54	(7)
Frequency Functions and Distribution Functions	55	(4)
Properties of Distributions	59	(2)
Sampling Distributions	61	(1)
Useful Distributions	62	(2)
Summary	64	(1)
Bibliographical Notes	65	(1)
Exercises	65	(3)
Bibliography	67	(1)
Interpretations of Probability	68	(30)
Introduction	68	(1)
The Classical View	68	(3)
Empirical Interpretations of Probability	71	(9)
The Limiting Frequency Interpretation	72	(6)
The Propensity Interpretation	78	(2)
Logical Interpretations of Probability	80	(7)
Subjective Interpretations of Probability	87	(6)
Dutch Book	87	(2)
Conditionalization	89	(4)
Summary	93	(2)
Bibliographical Notes	95	(1)
Exercises	95	(3)
Bibliography	96	(2)
Nonstandard Measures of Support	98	(19)
Support	98	(1)
Karl Popper	99	(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