Index
A logic, 10
A sublogic, 10
Abelian monoid, 89
Abelian semigroup, 89, 130
Absorbing element in a semigroup, 89
Acceptable program, xxiii, 26, 66, 76,
145, 158
Activation function, 188
Acyclic program, 141, 147-160, 165,
196
Addition unit, 217
Algebraicity, 3
Allowable values, 213
α-th layer, 46
α-th stratum, 46
Alphabet, 7
Alternating fixed-point model, 61
Answer set programming, xxi, 128,
135, 137
Antisymmetric relation, 1
Antitonic function, 5
Approximates up to ε, 190, 200, 204,
208, 212
Approximating T P up to level n, 200,
203
Approximating least fixed points, 209
Approximating networks exist, 190208, 218
Approximation in space, 197
Approximation in time, 197
Atom, 8
ground, 8
Atomic formula, 8
Ball in a continuity space, 90
Ball in a d-gum, 99, 104, 123-125, 148
Ball in a gum, 99, 100, 119, 130, 132
Banach contraction mapping theorem, xxiii, 93-108, 113-116, 140147, 166, 194
multivalued, 129, 134
Base for a topology, 235
Basic neighbourhood, 235
Basic open set, 66, 70, 74, 82
Becomes active at time t, 189, 193
Belnap’s four-valued logic, 10, 20, 83,
152, 165-167, 213
Bi-Cauchy sequence, 109
Binary threshold unit, 189-196, 215,
216
Body literal, 24, 45, 50, 62, 144, 162
Body of a clause, 24, 51, 145, 169, 200
Body of a pseudo-clause, 152, 164, 214
Both, 10
Bottom element, 2, 13, 74, 98, 122,
128, 192, 242
Bottom layer, 46, 51, 61
Bottom stratum, 46, 51, 54
Cantor topology, xxiii, 66, 79, 108,
143, 155, 161, 198
Cauchy sequence, 91-96
in a d-metric, 103, 116
in a quasimetric, 106-111, 133-135
Centre of a ball, 99
Chain complete, 2-5, 121-123
Chain in an ordered set, 1
Clark completion, xx, 32
Classical logic, xx, 9, 43, 165
Clause, 23
of finite type, 162
pseudo-, 152, 153, 164-167, 214
Closed ball about a point, 89
Closed set, 71, 236
265
A logic, 10
A sublogic, 10
Abelian monoid, 89
Abelian semigroup, 89, 130
Absorbing element in a semigroup, 89
Acceptable program, xxiii, 26, 66, 76,
145, 158
Activation function, 188
Acyclic program, 141, 147-160, 165,
196
Addition unit, 217
Algebraicity, 3
Allowable values, 213
α-th layer, 46
α-th stratum, 46
Alphabet, 7
Alternating fixed-point model, 61
Answer set programming, xxi, 128,
135, 137
Antisymmetric relation, 1
Antitonic function, 5
Approximates up to ε, 190, 200, 204,
208, 212
Approximating T P up to level n, 200,
203
Approximating least fixed points, 209
Approximating networks exist, 190208, 218
Approximation in space, 197
Approximation in time, 197
Atom, 8
ground, 8
Atomic formula, 8
Ball in a continuity space, 90
Ball in a d-gum, 99, 104, 123-125, 148
Ball in a gum, 99, 100, 119, 130, 132
Banach contraction mapping theorem, xxiii, 93-108, 113-116, 140147, 166, 194
multivalued, 129, 134
Base for a topology, 235
Basic neighbourhood, 235
Basic open set, 66, 70, 74, 82
Becomes active at time t, 189, 193
Belnap’s four-valued logic, 10, 20, 83,
152, 165-167, 213
Bi-Cauchy sequence, 109
Binary threshold unit, 189-196, 215,
216
Body literal, 24, 45, 50, 62, 144, 162
Body of a clause, 24, 51, 145, 169, 200
Body of a pseudo-clause, 152, 164, 214
Both, 10
Bottom element, 2, 13, 74, 98, 122,
128, 192, 242
Bottom layer, 46, 51, 61
Bottom stratum, 46, 51, 54
Cantor topology, xxiii, 66, 79, 108,
143, 155, 161, 198
Cauchy sequence, 91-96
in a d-metric, 103, 116
in a quasimetric, 106-111, 133-135
Centre of a ball, 99
Chain complete, 2-5, 121-123
Chain in an ordered set, 1
Clark completion, xx, 32
Classical logic, xx, 9, 43, 165
Clause, 23
of finite type, 162
pseudo-, 152, 153, 164-167, 214
Closed ball about a point, 89
Closed set, 71, 236
265