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Parametric Uniformity and Conditional Structures
Contents
Contents
Front
Erklärung
Dedication
Acknowledgement
Contents
Chapters
1
Introduction
1.1
Overview and Structure
p. 1
1.2
Definitions, Proofs and Assumptions
p. 4
2
Background
2.1
Probabilistic Conditional Knowledge Base
p. 5
2.2
Parametric Uniformity
p. 8
2.3
Conditional Structure
p. 11
2.4
Related Work
p. 17
3
Objectives and Initial Findings
3.1
Objectives
p. 19
3.2
Different Knowledge Bases Creating Same Conditional Structure
p. 21
3.3
Imbalanced Usage Cannot be Determined from a Conditional Structure
p. 22
3.4
Summary and Discussion
p. 24
4
Atomic Conditionals
4.1
Atomic Conditionals
p. 27
4.2
Negation
p. 28
4.3
Conditional Contribution
p. 28
4.4
Common Appearance
p. 29
4.5
vf-Pair Operations
p. 30
4.6
Maximum Ordered Sums
p. 31
4.7
Possible World Segments
p. 33
4.8
Atomic Counting Functions
p. 38
4.9
Types of Instantiation Restrictions
p. 43
5
Sums of vf–Pairs of CA-Conditionals
5.1
vf--Pairs of A-Segments in a CA-Conditional Without Non-Local Instantiation Restrictions
p. 48
5.2
vf-Pairs of A-Segments in a CA-Conditional With All Types Of Instantiation Restrictions
p. 52
6
Calculation of Conditional Contributions
6.1
Calculation of Conditional Contributions of C-Conditionals
p. 57
6.2
Calculation of Conditional Contributions of CA-Conditionals
p. 58
6.3
Calculation from CC-Conditionals and CAC-Conditionals
p. 60
6.4
Summary
p. 61
6.5
Excursion: Addition of Maximum Ordered Sums
p. 61
7
Reduction of C-Segments
7.1
Common Antecedence Sets
p. 64
7.2
Common Antecedence Segments
p. 67
7.3
Redundant Segments
p. 68
7.4
Set of Representatives
p. 71
7.5
Reduced Set of C-Segments
p. 73
8
RCS and Conditional Contributions
8.1
Generation of Conditional Contribution for CA-Conditionals
p. 77
8.2
Generation of Conditional Contribution for C-Conditionals
p. 78
8.3
Generation of Conditional Contribution for CC-Conditionals - ccRCS
p. 79
8.4
Equivalence Classes of Possible Worlds and RCS
p. 83
8.5
Effectiveness of the Method of Reduction of C-Segments
p. 84
8.6
Summary and Discussion
p. 86
8.7
Excursion: Grounding Tables
p. 87
9
Generation of Conditional Structure
9.1
Generation of Common Appearances
p. 90
9.2
Generation of Conditional Structures
p. 95
9.3
Summary and Discussion
p. 99
10
Interpreting Common Appearances
10.1
Definitions
p. 101
10.2
Complete CA-Tables
p. 102
10.3
Single Lines
p. 106
10.4
Imbalanced Sharing and CA-Tables
p. 112
10.5
Determining Imbalanced Sharing
p. 114
10.6
Summary and Discussion
p. 114
11
Transformation of a Conditional Structure
11.1
Initial Definitions and Basic Example
p. 115
11.2
Transformation
p. 118
11.3
Discussion
p. 119
12
Summary
Back
Acronyms
Glossary
Bibliography
List of Figures
List of Tables
List of Definitions
List of Propositions
List of Assumptions
List of Examples
Index
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Acknowledgement
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Introduction