266
Closure of a set, 236
Closure operator, 67, 68, 236
Closure ordinal, 7, 41
Coarser topology, 234
Commutative monoid, 89
Commutative semigroup, 89
Compact element, 3, 14, 69, 119, 240
Compact topological space, 239
Comparable elements, 1, 242
Complete d-metric space, 103, 115
Complete lattice, 2, 61, 75, 125, 181
Complete partial order, 2, 69, 126, 170
Complete upper semi-lattice, 2, 13
Completeness in metric spaces, 91
Component, 45
minimal, 46
trivial, 45
Conjunction, xix, 10, 24, 152, 214
Connectionist network, 188
Connectionist system, 185, 188, 198
Connectives, 8, 10, 154, 161
Consequence operator, 161-166, 213
locally finite, 163
Consistent completeness, 3, 120
Consistent signed subset, 19
Continuity function, 90-92, 98
Continuity of a function, 237
at a point, 68, 237
Continuity space, 88-92, 98
Continuous function, 5, 68, 133, 204,
237
Contraction mapping, 93, 114
multivalued, 129
multivalued on a quasimetric, 133
on a d-metric, 103
on a quasimetric, 106, 107
Contractive, 106, 144
Contractivity factor, 93, 114-119, 144
Convergence class, xxiii, 67-72, 77, 78
Convergence in a d-metric, 103
Convergence in a quasimetric, 106
Convergence space, xxiii, 67, 68
Convergent net, 67, 237
Converges to, 67, 237
Core method, 187, 192, 220
Index
Covered logic program, 200-208
Cpo, 2
CS-complete quasimetric space, 106108
CS-continuous function, 106-111
d-gum space, 97
d-metric, 91, 92, 102
Declarative semantics, xxi, 15, 23,
137, 186
Definite logic program, 24
Denotation of a term, 11
Denotational semantics, xxii, 4, 221224
Dependency graph, 45-48
Depends negatively on, 45
Depends on, 45, 144
Directed set, 2, 237
Discrete quasimetric, 107, 108
Discrete topology, 77, 78, 82, 100, 235
Disjunction, 10, 214
Disjunctive logic programs, xix, 125,
130, 135
Dislocated generalized ultrametric space,
97, 104
Dislocated metric, 91, 92, 102
Dislocation function, 114
Distance function, 88-91
d-gum, 97
d-metric, 91, 92, 102
g-metric, 130-132
gum, 92, 97
metric, 91
pseudometric, 91
quasimetric, 91
ultrametric, xxv, 91
Distance set, 88, 100, 121
DLV system, xix, 169
Domain, 3, 4, 69, 118, 136, 222, 240
Scott, 3
Scott-Ershov, 3
Domain of a preinterpretation, 11, 26
Downwards closed set, 75
Dual ordering, 2, 119
Egli–Milner monotonicity, 126
Closure of a set, 236
Closure operator, 67, 68, 236
Closure ordinal, 7, 41
Coarser topology, 234
Commutative monoid, 89
Commutative semigroup, 89
Compact element, 3, 14, 69, 119, 240
Compact topological space, 239
Comparable elements, 1, 242
Complete d-metric space, 103, 115
Complete lattice, 2, 61, 75, 125, 181
Complete partial order, 2, 69, 126, 170
Complete upper semi-lattice, 2, 13
Completeness in metric spaces, 91
Component, 45
minimal, 46
trivial, 45
Conjunction, xix, 10, 24, 152, 214
Connectionist network, 188
Connectionist system, 185, 188, 198
Connectives, 8, 10, 154, 161
Consequence operator, 161-166, 213
locally finite, 163
Consistent completeness, 3, 120
Consistent signed subset, 19
Continuity function, 90-92, 98
Continuity of a function, 237
at a point, 68, 237
Continuity space, 88-92, 98
Continuous function, 5, 68, 133, 204,
237
Contraction mapping, 93, 114
multivalued, 129
multivalued on a quasimetric, 133
on a d-metric, 103
on a quasimetric, 106, 107
Contractive, 106, 144
Contractivity factor, 93, 114-119, 144
Convergence class, xxiii, 67-72, 77, 78
Convergence in a d-metric, 103
Convergence in a quasimetric, 106
Convergence space, xxiii, 67, 68
Convergent net, 67, 237
Converges to, 67, 237
Core method, 187, 192, 220
Index
Covered logic program, 200-208
Cpo, 2
CS-complete quasimetric space, 106108
CS-continuous function, 106-111
d-gum space, 97
d-metric, 91, 92, 102
Declarative semantics, xxi, 15, 23,
137, 186
Definite logic program, 24
Denotation of a term, 11
Denotational semantics, xxii, 4, 221224
Dependency graph, 45-48
Depends negatively on, 45
Depends on, 45, 144
Directed set, 2, 237
Discrete quasimetric, 107, 108
Discrete topology, 77, 78, 82, 100, 235
Disjunction, 10, 214
Disjunctive logic programs, xix, 125,
130, 135
Dislocated generalized ultrametric space,
97, 104
Dislocated metric, 91, 92, 102
Dislocation function, 114
Distance function, 88-91
d-gum, 97
d-metric, 91, 92, 102
g-metric, 130-132
gum, 92, 97
metric, 91
pseudometric, 91
quasimetric, 91
ultrametric, xxv, 91
Distance set, 88, 100, 121
DLV system, xix, 169
Domain, 3, 4, 69, 118, 136, 222, 240
Scott, 3
Scott-Ershov, 3
Domain of a preinterpretation, 11, 26
Downwards closed set, 75
Dual ordering, 2, 119
Egli–Milner monotonicity, 126