274
Two-valued valuation, 18
Tychonoff’s theorem, 240
Ultrametric, xxv, 91
Ultrametric induced by a rank function, 119
Undefined, 20
Underdefined, 9
Underlying first-order language, 24
Underlying language, 24
Unfolding, 169-172
Unfounded set, 57-60
Unique supported model class, xxvi,
139
Uniquely determined program, 139
Unit clause, 24
Unit in a neural network, 188
addition, 217
binary threshold, 189-196, 215, 216
linear, 189
multiplication, 215-217
sigmoidal, 189
squashing, 189
Upper bound, 2, 121, 135, 196
least, 2, 121, 135
Upwards closed set, 69, 240
v-Cauchy, 131
v-cluster, 131
v-complete g-metric, 131
v-complete subset, 131
Index
Valuation, 12, 13, 28, 161
finite, 13
four-valued, 18
three-valued, 18
two-valued, 18
Value of a node, 188
Value semigroup, 89
Value set, 88
Variable assignment, 11
Vector-based network, 207
Weak partial metric, 102
Weak stratification, 45, 48
Weaker topology, 234
Weakly perfect model, 45-63, 182, 183
Weakly perfect semantics, 45-63
Weakly stratified program, 48
Web Ontology Language OWL, 224
Weight function, 114, 146
Well-formed formula, xxi, 8-12
Well-founded model, xxi, 57-64, 170175
Well-founded semantics, 57-61, 170,
225
Well-ordered set, 229
Well-ordering, 229
Well-Ordering Theorem, 231
Well-supported interpretation, 33
Well-supported model, 33
Winner unit, 208
W P -operator, 57
Two-valued valuation, 18
Tychonoff’s theorem, 240
Ultrametric, xxv, 91
Ultrametric induced by a rank function, 119
Undefined, 20
Underdefined, 9
Underlying first-order language, 24
Underlying language, 24
Unfolding, 169-172
Unfounded set, 57-60
Unique supported model class, xxvi,
139
Uniquely determined program, 139
Unit clause, 24
Unit in a neural network, 188
addition, 217
binary threshold, 189-196, 215, 216
linear, 189
multiplication, 215-217
sigmoidal, 189
squashing, 189
Upper bound, 2, 121, 135, 196
least, 2, 121, 135
Upwards closed set, 69, 240
v-Cauchy, 131
v-cluster, 131
v-complete g-metric, 131
v-complete subset, 131
Index
Valuation, 12, 13, 28, 161
finite, 13
four-valued, 18
three-valued, 18
two-valued, 18
Value of a node, 188
Value semigroup, 89
Value set, 88
Variable assignment, 11
Vector-based network, 207
Weak partial metric, 102
Weak stratification, 45, 48
Weaker topology, 234
Weakly perfect model, 45-63, 182, 183
Weakly perfect semantics, 45-63
Weakly stratified program, 48
Web Ontology Language OWL, 224
Weight function, 114, 146
Well-formed formula, xxi, 8-12
Well-founded model, xxi, 57-64, 170175
Well-founded semantics, 57-61, 170,
225
Well-ordered set, 229
Well-ordering, 229
Well-Ordering Theorem, 231
Well-supported interpretation, 33
Well-supported model, 33
Winner unit, 208
W P -operator, 57
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