272
RBF network, 204
Recurrent network, 190
Reduct of P with respect to I, 46
Refers negatively to, 45
Refers to, 45, 144
Reflexive relation, 1
Relation, 1
antisymmetric, 1
reflexive, 1
transitive, 1
Relative topology, 239
Required values, 213
Resolution, xix, 31
Rule, 23
Rutten-Smyth theorem, 107
multivalued, 133
S-monotonic, 126
Scott continuous function, xxii, 72,
74, 170
Scott domain, 3
Scott open set, 69-71, 242
Scott topology, xxiii, 69-76, 234
Scott-Ershov domain, 3
Semantic operator, xxii, 10, 66, 126,
136, 161, 186
Semantic Web, xix, 223
Semantics, xx
declarative, xxi, 15, 23, 137, 186
denotational, xxii, 4, 221-224
Fitting, 37, 42, 55, 56, 150, 156
fixed-point, xxii
Kripke-Kleene, 37
least model, 31
operational, xxi
perfect model, 44, 175-183
procedural, xxi, xxiii, 29
stable model, 34, 36, 37, 43, 171
weakly perfect, 45-63
well-founded, 57-61, 170, 225
Semigroup, 89
Semigroup with identity, 89
Set of positives, 90
Set of truth values, 10
σ-algebra, 167
Index
Sigmoidal network, 201
Sigmoidal unit, 189
Signed subset, 13, 19, 20, 37, 46, 154
Single-step operator, xxiii, 29, 80, 140,
155, 171, 218
Single-valued function, 129, 133, 134
Single-valued mapping, 129, 133, 134
SLD-resolution, xix, 147
SLDNF-resolution, xix, 32, 141, 144
Smodels system, xix, 169
Smyth monotonicity, 126, 137
Smyth ordering, 126
Space of formal balls, 121
Spherically complete (d-)gum, 99
Squashing functions, 189
Squashing unit, 189
Stable model, xxi, 33-37, 43-46, 62,
130-136, 169-174, 219
Stable model semantics, 34, 36, 37, 43,
171
Stratified program, 44
Strictly contracting function on a
metric, 94
Strictly contracting function on a
(d-)gum, 99
Strictly contracting multivalued function on a (d-)gum, 129
Strictly contracting function on orbits, 99
Strictly contracting multivalued function on orbits, 129
Strong triangle inequality, 92
Strong triangle inequality for gums,
98
Stronger topology, 234
Subbase for a topology, 74, 82, 167,
235
Subbasic open set, 82, 163
Subnet of a net, 237
Subspace topology, 239
Subsumes, 50
Subsumes model-consistently, 50
Successor notation, 25-27
Successor ordinal, 232
Supported interpretation, 31-33
RBF network, 204
Recurrent network, 190
Reduct of P with respect to I, 46
Refers negatively to, 45
Refers to, 45, 144
Reflexive relation, 1
Relation, 1
antisymmetric, 1
reflexive, 1
transitive, 1
Relative topology, 239
Required values, 213
Resolution, xix, 31
Rule, 23
Rutten-Smyth theorem, 107
multivalued, 133
S-monotonic, 126
Scott continuous function, xxii, 72,
74, 170
Scott domain, 3
Scott open set, 69-71, 242
Scott topology, xxiii, 69-76, 234
Scott-Ershov domain, 3
Semantic operator, xxii, 10, 66, 126,
136, 161, 186
Semantic Web, xix, 223
Semantics, xx
declarative, xxi, 15, 23, 137, 186
denotational, xxii, 4, 221-224
Fitting, 37, 42, 55, 56, 150, 156
fixed-point, xxii
Kripke-Kleene, 37
least model, 31
operational, xxi
perfect model, 44, 175-183
procedural, xxi, xxiii, 29
stable model, 34, 36, 37, 43, 171
weakly perfect, 45-63
well-founded, 57-61, 170, 225
Semigroup, 89
Semigroup with identity, 89
Set of positives, 90
Set of truth values, 10
σ-algebra, 167
Index
Sigmoidal network, 201
Sigmoidal unit, 189
Signed subset, 13, 19, 20, 37, 46, 154
Single-step operator, xxiii, 29, 80, 140,
155, 171, 218
Single-valued function, 129, 133, 134
Single-valued mapping, 129, 133, 134
SLD-resolution, xix, 147
SLDNF-resolution, xix, 32, 141, 144
Smodels system, xix, 169
Smyth monotonicity, 126, 137
Smyth ordering, 126
Space of formal balls, 121
Spherically complete (d-)gum, 99
Squashing functions, 189
Squashing unit, 189
Stable model, xxi, 33-37, 43-46, 62,
130-136, 169-174, 219
Stable model semantics, 34, 36, 37, 43,
171
Stratified program, 44
Strictly contracting function on a
metric, 94
Strictly contracting function on a
(d-)gum, 99
Strictly contracting multivalued function on a (d-)gum, 129
Strictly contracting function on orbits, 99
Strictly contracting multivalued function on orbits, 129
Strong triangle inequality, 92
Strong triangle inequality for gums,
98
Stronger topology, 234
Subbase for a topology, 74, 82, 167,
235
Subbasic open set, 82, 163
Subnet of a net, 237
Subspace topology, 239
Subsumes, 50
Subsumes model-consistently, 50
Successor notation, 25-27
Successor ordinal, 232
Supported interpretation, 31-33