269
Index
Local consequence operator, 162-166,
213, 218
Local variable, 162, 163, 173, 200
Locally finite consequence operator,
163
Locally hierarchical program, 141147, 156, 174, 179-181
Locally stratified program, 44
Logic program, 23, 24
ω-locally hierarchical, 141
Φ-accessible, 139, 150, 151
Φ
∗ -accessible, 147-150
acceptable, xxiii, 26, 66, 76, 145,
158
acyclic, 141, 147-160, 165, 196
covered, 200-208
definite, 24
disjunctive, xix, 125, 130, 135
locally hierarchical, 141-147, 156,
174, 179-181
locally stratified, 44
normal, 24
of finite type, 162
positive, 24
propositional, 24-27, 187, 192, 217
satisfies (F) with respect to I and
l, 41, 150, 151
satisfies (F 12 ) with respect to I and
l, 159
satisfies (F 22 ) with respect to I and
l, 158
satisfies (F 32 ) with respect to I and
l, 156
satisfies (WF) with respect to I
and l, 56
satisfies (WS) with respect to I and
l, 49
stratified, 44
uniquely determined, 139
weakly stratified, 48
Logic programming, xix
Logic, 9
classical, xx, 9, 43, 165
four-valued, 10, 165
Kleene’s strong three-valued, 9, 37,
48, 57, 152, 165, 213
three-valued, 9
two-valued, 9, 10
Lower bound, 2, 130
greatest, 2
Matthews’ theorem, 103, 104, 114,
115, 118, 147
Maximal element, 2-4, 122
Metric, 91
Metric associated with a d-metric,
117, 118
Metric domain, 102
Metric induced by a quasimetric, 106
Metrizable space, 79
Midpoint of a ball, 99
Minimal component, 46
Minimal element, 2, 129
Minimal model, 30-34
Model, 12, 28
alternating fixed point, 61
Fitting, 39-44, 55, 63, 139, 151, 174
intended, 23, 30, 45, 55
Kripke-Kleene, 39
least, 30-35, 76, 196
minimal, 30-34
perfect, xxiv, 43-45, 175-183
stable, xxi, 33-37, 43-46, 62, 130136, 169-174, 219
supported, xxi, 31-33
three-valued supported, 40, 151
weakly perfect, 45-63, 182, 183
well-founded, xxi, 57-64, 170-175
well-supported, 33
Monotonic function, 5, 230
Multilayer feedforward network, 189191
Multiplication unit, 215-217
Multivalued contraction mapping, 129
Multivalued mapping, 125, 222
ω-continuous, 135
ω-orbit of, 127, 133-135
continuous on a quasimetric, 133
contraction, 129
Index
Local consequence operator, 162-166,
213, 218
Local variable, 162, 163, 173, 200
Locally finite consequence operator,
163
Locally hierarchical program, 141147, 156, 174, 179-181
Locally stratified program, 44
Logic program, 23, 24
ω-locally hierarchical, 141
Φ-accessible, 139, 150, 151
Φ
∗ -accessible, 147-150
acceptable, xxiii, 26, 66, 76, 145,
158
acyclic, 141, 147-160, 165, 196
covered, 200-208
definite, 24
disjunctive, xix, 125, 130, 135
locally hierarchical, 141-147, 156,
174, 179-181
locally stratified, 44
normal, 24
of finite type, 162
positive, 24
propositional, 24-27, 187, 192, 217
satisfies (F) with respect to I and
l, 41, 150, 151
satisfies (F 12 ) with respect to I and
l, 159
satisfies (F 22 ) with respect to I and
l, 158
satisfies (F 32 ) with respect to I and
l, 156
satisfies (WF) with respect to I
and l, 56
satisfies (WS) with respect to I and
l, 49
stratified, 44
uniquely determined, 139
weakly stratified, 48
Logic programming, xix
Logic, 9
classical, xx, 9, 43, 165
four-valued, 10, 165
Kleene’s strong three-valued, 9, 37,
48, 57, 152, 165, 213
three-valued, 9
two-valued, 9, 10
Lower bound, 2, 130
greatest, 2
Matthews’ theorem, 103, 104, 114,
115, 118, 147
Maximal element, 2-4, 122
Metric, 91
Metric associated with a d-metric,
117, 118
Metric domain, 102
Metric induced by a quasimetric, 106
Metrizable space, 79
Midpoint of a ball, 99
Minimal component, 46
Minimal element, 2, 129
Minimal model, 30-34
Model, 12, 28
alternating fixed point, 61
Fitting, 39-44, 55, 63, 139, 151, 174
intended, 23, 30, 45, 55
Kripke-Kleene, 39
least, 30-35, 76, 196
minimal, 30-34
perfect, xxiv, 43-45, 175-183
stable, xxi, 33-37, 43-46, 62, 130136, 169-174, 219
supported, xxi, 31-33
three-valued supported, 40, 151
weakly perfect, 45-63, 182, 183
well-founded, xxi, 57-64, 170-175
well-supported, 33
Monotonic function, 5, 230
Multilayer feedforward network, 189191
Multiplication unit, 215-217
Multivalued contraction mapping, 129
Multivalued mapping, 125, 222
ω-continuous, 135
ω-orbit of, 127, 133-135
continuous on a quasimetric, 133
contraction, 129