268
Ground instance of a clause, 26
Ground instance of an atom, 11, 26
Ground term, 8
Gum, 92, 97
Gum associated with a d-gum, 123
Gum induced by a rank function, 119
Gum with ordinal distances, 121, 142
A b
1
-contraction, 131
2
Hausdorff space, 239
Head of a clause, 24
Head of a list, 26
Head of a pseudo-clause, 152
Herbrand preinterpretation, 26
Herbrand universe, 26
Hidden layer, 189
Hoare monotonicity, 126-128, 135
Hoare ordering, 126
I-partial level mapping, 40
Identity of a semigroup, 89
Immediate consequence operator, 29,
42, 66, 74, 110, 146, 196
Immediate consequence operator restricted at level n, 175
Implication, 10, 16
Incomparable elements, 1, 10, 242
Increasing orbit, 127
Indiscrete topology, 235
Infimum, 2
Initial segment, 230, 231
proper, 230
Input layer, 189-191
Input vector, 188, 189
Input-output mapping, 189, 190
Intended model, 23, 30, 45, 55
Interior of a set, 236
Interpretation, 12, 28, 161, 167, 191,
198
four-valued, 18-20, 28
partial, 19
supported, 31-33
three-valued, 18, 28
total, 19, 42
two-valued, xxvii, 18, 19, 28
Index
well-supported, 33
Isomorphic well-orderings, 230
Iterates of a function, 5
J-ground instance of a clause, 26
J-ground instance of an atom, 11
k-safe clause, 158
Kernel of a neural network, 190
Kleene’s strong three-valued logic, 9,
37, 48, 57, 152, 165, 213
Kleene’s theorem, xxiii, 6, 7
multivalued, 135
Kleene’s weak three-valued logic, 9, 11
Knaster-Tarski theorem, 6, 7
multivalued, 128
Knowledge ordering, 10, 16, 37
Knowledge Representation and Reasoning, xix, 223
Kripke-Kleene model, 39
Kripke-Kleene semantics, 37
Layer in a network, 189
hidden, 189
input, 189-191
output, 189-191
Least element, 2, 97, 126, 215, 229
Least fixed point, 5, 30, 209
Least infinite ordinal, 233
Least model, 30-35, 76, 196
Least model semantics, 31
Least post-fixed point, 6
Least pre-fixed point, 6
Least upper bound, 2, 121, 135
Length, 25, 26
Level mapping, 33, 44, 109-112, 142,
174, 198
Limit of a net, 237
Limit of a sequence in a d-metric, 103
Limit ordinal, 1, 5, 62, 98, 127, 232234
Linear unit, 189
List, 26
Literal, 8
negative, 8
positive, 8
Ground instance of a clause, 26
Ground instance of an atom, 11, 26
Ground term, 8
Gum, 92, 97
Gum associated with a d-gum, 123
Gum induced by a rank function, 119
Gum with ordinal distances, 121, 142
A b
1
-contraction, 131
2
Hausdorff space, 239
Head of a clause, 24
Head of a list, 26
Head of a pseudo-clause, 152
Herbrand preinterpretation, 26
Herbrand universe, 26
Hidden layer, 189
Hoare monotonicity, 126-128, 135
Hoare ordering, 126
I-partial level mapping, 40
Identity of a semigroup, 89
Immediate consequence operator, 29,
42, 66, 74, 110, 146, 196
Immediate consequence operator restricted at level n, 175
Implication, 10, 16
Incomparable elements, 1, 10, 242
Increasing orbit, 127
Indiscrete topology, 235
Infimum, 2
Initial segment, 230, 231
proper, 230
Input layer, 189-191
Input vector, 188, 189
Input-output mapping, 189, 190
Intended model, 23, 30, 45, 55
Interior of a set, 236
Interpretation, 12, 28, 161, 167, 191,
198
four-valued, 18-20, 28
partial, 19
supported, 31-33
three-valued, 18, 28
total, 19, 42
two-valued, xxvii, 18, 19, 28
Index
well-supported, 33
Isomorphic well-orderings, 230
Iterates of a function, 5
J-ground instance of a clause, 26
J-ground instance of an atom, 11
k-safe clause, 158
Kernel of a neural network, 190
Kleene’s strong three-valued logic, 9,
37, 48, 57, 152, 165, 213
Kleene’s theorem, xxiii, 6, 7
multivalued, 135
Kleene’s weak three-valued logic, 9, 11
Knaster-Tarski theorem, 6, 7
multivalued, 128
Knowledge ordering, 10, 16, 37
Knowledge Representation and Reasoning, xix, 223
Kripke-Kleene model, 39
Kripke-Kleene semantics, 37
Layer in a network, 189
hidden, 189
input, 189-191
output, 189-191
Least element, 2, 97, 126, 215, 229
Least fixed point, 5, 30, 209
Least infinite ordinal, 233
Least model, 30-35, 76, 196
Least model semantics, 31
Least post-fixed point, 6
Least pre-fixed point, 6
Least upper bound, 2, 121, 135
Length, 25, 26
Level mapping, 33, 44, 109-112, 142,
174, 198
Limit of a net, 237
Limit of a sequence in a d-metric, 103
Limit ordinal, 1, 5, 62, 98, 127, 232234
Linear unit, 189
List, 26
Literal, 8
negative, 8
positive, 8