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Tables of Contents for Probabilistic Logic in a Coherent Setting
Chapter/Section Title
Page #
Page Count
Introduction
7
10
Aims and motivation
7
5
A brief historical perspective
12
5
Events as Propositions
17
8
Basic concepts
17
1
From ``belief'' to logic?
18
2
Operations
20
1
Atoms (or ``possible worlds'')
21
3
Toward probability
24
1
Finitely Additive Probability
25
6
Axioms
25
1
Sets (of events) without structure
26
1
Null probabilities
27
4
Coherent probability
31
6
Coherence
31
3
Null probabilities (again)
34
3
Betting Interpretation of Coherence
37
6
Coherent Extensions of Probability Assessments
43
6
de Finetti's fundamental theorem
43
2
Probabilistic logic and inference
45
4
Random Quantities
49
4
Probability Meaning and Assessment: a Reconciliation
53
4
The ``subjective'' view
53
2
Methods of evaluation
55
2
To Be or not To Be Compositional?
57
4
Conditional Events
61
12
Truth values
63
2
Operations
65
5
Toward conditional probability
70
3
Coherent Conditional Probability
73
26
Axioms
73
1
Assumed or acquired conditioning?
74
2
Coherence
76
4
Characterization of a coherent conditional probability
80
10
Related results
90
4
The role of probabilities 0 and 1
94
5
Zero-Layers
99
10
Zero-layers induced by a coherent conditional probability
99
2
Spohn's ranking function
101
1
Discussion
102
7
Coherent Extensions of Conditional Probability
109
8
Exploiting Zero Probabilities
117
10
The algorithm
117
5
Locally strong coherence
122
5
Lower and Upper Conditional Probabilities
127
10
Coherence intervals
127
1
Lower conditional probability
128
6
Dempster's theory
134
3
Inference
137
26
The general problem
137
2
The procedure at work
139
12
Discussion
151
4
Updating probabilities 0 and 1
155
8
Stochastic Independence in a Coherent Setting
163
28
``Precise'' probabilities
164
15
``Imprecise'' probabilities
179
7
Discussion
186
4
Concluding remarks
190
1
A Random Walk in the Midst of Paradigmatic Examples
191
24
Finite additivity
191
2
Stochastic independence
193
1
A not coherent ``Radon-Nikodym'' conditional probability
194
3
A changing ``world''
197
1
Frequency vs. probability
198
4
Acquired or assumed (again)
202
1
Choosing the conditioning event
202
2
Simpson's paradox
204
2
Belief functions
206
9
Fuzzy Sets and Possibility as Coherent Conditional Probabilities
215
26
Fuzzy sets: main definitions
216
3
Fuzziness and uncertainty
219
6
Fuzzy subsets and coherent conditional probability
225
7
Possibility functions and coherent conditional probability
232
8
Concluding remarks
240
1
Coherent Conditional Probability and Default Reasoning
241
16
Default logic through conditional probability equal to 1
243
4
Inferential rules
247
4
Discussion
251
6
A Short Account of Decomposable Measures of Uncertainty
257
14
Operations with conditional events
258
4
Decomposable measures
262
4
Weakly decomposable measures
266
4
Concluding remarks
270
1
Bibliography
271
14
Index
285