Index
271
Smyth, 126
truth, 10, 15, 16
Ordinal, 2, 231
closure, 7, 41
first infinite, 233
least infinite, 233
limit, 1, 5, 62, 98, 127, 232-234
predecessor, 232
successor, 232
Ordinal number, 231
Ordinal powers of a function, 5
Output function, 189, 190
Output layer, 189-191
Overdefined, 10
P
− , 145
P -local consequence operator, 162166, 213, 218
Partial interpretation, 19
Partial metric, 102
Partial order, 1-6
Partial order induced by +, 90
Partial order induced by a quasimetric, 106
Partially ordered set, 1-3
Perfect model, xxiv, 43-45, 175-183
Perfect model semantics, 44, 175-183
Φ-accessible program, 139, 150, 151
Φ
∗ -accessible program, 147-150
Φ P -operator, 37
Φ P,j,k -operator, 154
Poset, 1
Positive literal, 8
Positive logic program, 24
Post-fixed point, 5
Potential, 188
Powers of an operator, 181
Pre-fixed point, 5
Predecessor of an ordinal, 232
Preference between models, 44, 180,
181
Preinterpretation, 11, 26
Prieß-Crampe and Ribenboim theorem, 100
Prieß-Crampe and Ribenboim theorem multivalued, 130
Principle of Transfinite Induction, 233
Procedural aspects, xxv, 29
Procedural semantics, xxi, xxiii, 29
Product topology, 80, 82, 162, 239
projection on the j-th factor of, 239
Program, 24
see also Logic program
Program clause, 23
Prolog, xix, 25, 141, 144
Proper initial segment, 230
Proposition, 8
Propositional approximation, 187, 199
Propositional logic program, 24, 25,
27, 187, 192, 217
P satisfies (F) with respect to I and
l, 41, 150, 151
P satisfies (F 12 ) with respect to I and
l, 159
P satisfies (F 22 ) with respect to I and
l, 158
P satisfies (F 32 ) with respect to I and
l, 156
P satisfies (WF) with respect to I and
l, 56
P satisfies (WS) with respect to I and
l, 49
Pseudo-clause, 152, 153, 164-167, 214
body of, 152, 164, 214
head of, 152
Pseudo-convergent transfinite sequence,
101
Pseudo-limit of a transfinite sequence,
101
Pseudometric, 91
Quantitative domain theory, xxvii,
222, 225
Quasi-interpretation, 169, 170
Quasimetric, 91
Quasimetric induced by a rank function, 109
Rank function, 109, 119
271
Smyth, 126
truth, 10, 15, 16
Ordinal, 2, 231
closure, 7, 41
first infinite, 233
least infinite, 233
limit, 1, 5, 62, 98, 127, 232-234
predecessor, 232
successor, 232
Ordinal number, 231
Ordinal powers of a function, 5
Output function, 189, 190
Output layer, 189-191
Overdefined, 10
P
− , 145
P -local consequence operator, 162166, 213, 218
Partial interpretation, 19
Partial metric, 102
Partial order, 1-6
Partial order induced by +, 90
Partial order induced by a quasimetric, 106
Partially ordered set, 1-3
Perfect model, xxiv, 43-45, 175-183
Perfect model semantics, 44, 175-183
Φ-accessible program, 139, 150, 151
Φ
∗ -accessible program, 147-150
Φ P -operator, 37
Φ P,j,k -operator, 154
Poset, 1
Positive literal, 8
Positive logic program, 24
Post-fixed point, 5
Potential, 188
Powers of an operator, 181
Pre-fixed point, 5
Predecessor of an ordinal, 232
Preference between models, 44, 180,
181
Preinterpretation, 11, 26
Prieß-Crampe and Ribenboim theorem, 100
Prieß-Crampe and Ribenboim theorem multivalued, 130
Principle of Transfinite Induction, 233
Procedural aspects, xxv, 29
Procedural semantics, xxi, xxiii, 29
Product topology, 80, 82, 162, 239
projection on the j-th factor of, 239
Program, 24
see also Logic program
Program clause, 23
Prolog, xix, 25, 141, 144
Proper initial segment, 230
Proposition, 8
Propositional approximation, 187, 199
Propositional logic program, 24, 25,
27, 187, 192, 217
P satisfies (F) with respect to I and
l, 41, 150, 151
P satisfies (F 12 ) with respect to I and
l, 159
P satisfies (F 22 ) with respect to I and
l, 158
P satisfies (F 32 ) with respect to I and
l, 156
P satisfies (WF) with respect to I and
l, 56
P satisfies (WS) with respect to I and
l, 49
Pseudo-clause, 152, 153, 164-167, 214
body of, 152, 164, 214
head of, 152
Pseudo-convergent transfinite sequence,
101
Pseudo-limit of a transfinite sequence,
101
Pseudometric, 91
Quantitative domain theory, xxvii,
222, 225
Quasi-interpretation, 169, 170
Quasimetric, 91
Quasimetric induced by a rank function, 109
Rank function, 109, 119