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List of Examples

71 examples, in the order the thesis prints them.

1
Grounding of a Knowledge Base
Page 6
2
Sets of Groundings and Ground Atoms
Page 7
3
Imbalanced Sharing
Page 9
4
Balanced Functions
Page 10
5
Transformation Rules
Page 10
6
Possible Worlds
Page 12
7
vf-Pairs
Page 14
8
Conditional Impact
Page 15
9
Conditional Structure
Page 16
10
Equivalence Classes of Possible Worlds
Page 17
11
No One-to-One Relation Between Conditional Structures and Knowledge Bases
Page 22
12
Imbalanced Usage Cannot be Determined from CS
Page 22
13
Conditional Contribution
Page 29
14
Common Appearance
Page 29
15
Common Appearance Table
Page 30
16
vf-Pair Addition
Page 30
17
vf-Pair Scalar Multiplication
Page 31
18
Maximum Ordered Sums
Page 32
19
Multiples of a MOS (Scalar Multiplication)
Page 32
20
Conditional Contributions and MOS
Page 32
21
Possible World Segments
Page 34
22
Canonical and Composed Segments
Page 35
23
Dependency Between C- and A-Segments
Page 36
24
Semantical Combination of Possible Worlds
Page 37
25
Semantical Combination Function
Page 37
26
Semantical Combination Function for Sets of Possible Worlds
Page 38
27
Equality of Counting Function Definitions
Page 40
28
Types of Instantiation Restrictions
Page 43
29
Local and Non-Local Instantiation Restrictions
Page 45
30
vf-Pairs of A-Segments in a CA-Conditional without Instantiation Restrictions
Page 51
31
Reduced vf Truth Tables
Page 52
32
Set of C-Atoms Counted by an A-Atom
Page 53
33
vf-Pairs of A-Segments in a CA-Conditional
Page 54
34
Canonical A-Segments of CA-Conditionals Generate Maximum Ordered Sum
Page 56
35
Maximum Ordered Sum of a C-Conditional
Page 58
36
Maximum Ordered Sum of a CA-Conditional
Page 59
37
Set of A-Atoms Counting a C-atom
Page 65
38
Common Antecedence Set
Page 65
39
Common Antecedence Sets Cover Exactly All C-Atoms
Page 67
40
Common Antecedence Segment
Page 68
41
Redundant Segments
Page 69
42
Sequence of Truth Values in a Set of Redundant Segments
Page 70
43
Set of Representative
Page 71
44
Reduced Set of C-Segments
Page 73
45
Reduced Set of C-Segments and Conditional Contribution
Page 75
46
RCS Generates Conditional Contribution of C-Conditionals
Page 78
47
ccRCS Generates Conditional Contribution of CC-Conditionals - Identical C-Atoms and A-Atoms
Page 80
48
ccRCS Generates Conditional Contribution of CC-Conditionals - Different C-Atoms and A-Atoms
Page 82
49
RCS and Equivalence Classes of Possible Worlds
Page 83
50
$V\neq W$ Type Instantiation Restriction And Common Antecedence Sets
Page 85
51
$V=W$ Type Instantiation Restriction And Common Antecedence Sets
Page 85
52
Grounding Table
Page 87
53
Grounding Table Indicates Imbalanced Use
Page 88
54
Creating CA-Tables – Different Antecedence Predicates
Page 91
55
Creating CA-Tables – Same Antecedence Predicates
Page 93
56
Combining Common Appearances to Conditional Structures
Page 96
57
Predicates, Variables and Sorts Used in Chapter 10
Page 102
58
$C_1$ - $C_2$ Case
Page 103
59
$C_1$ - $C_2$ -localIR Case
Page 104
60
$C_1A_1$ - $C_2A_2$ -localIR Case
Page 105
61
$C_1$ - $C_1$ Case
Page 106
62
$C_1A_1$ - $C_1A_2$ Case
Page 107
63
$C_1A_1$ - $C_1A_2$ -2nolocalIR Case
Page 109
64
$C_1A_1$ - $A_1A_2$ Case
Page 110
65
$C_1A_1$ - $C_2C_1$ Case
Page 110
66
$C_1A_1$ - $C_2A_1$ Case
Page 111
67
$C_1$ - $C_1$ -IRc1c Case
Page 112
68
$C_1A_1$ - $C_1A_2$ -IRc1c Case
Page 113
69
$C_1A_1$ - $C_2A_1$ -IRa1c Case
Page 113
70
Transformation of Conditional Structure - Basic Example
Page 116
71
Transformation
Page 118