Index
267
Egli–Milner ordering, 126
Embedding of well-ordered sets, 230
Even, 25, 27, 140
Even2, 197
Eventually, 237
Eventually increasing orbit, 127
Excluded values, 213
ExistsEven, 141
Fact, 24
False, 9, 20, 161
Family of networks computes I, 212
Finer topology, 234
Finite element, 3
Finite valuation, 13
Finitely determined conjunction, 215
Finitely determined disjunction, 167,
215
Finitely determined operation, 213
First infinite ordinal, 233
First-order language, 9
Fitting model, 39-44, 55, 63, 139, 151,
174
Fitting operator, 37, 42, 43, 75, 151,
152, 161, 174
Fitting semantics, 37, 42, 55, 56, 150,
156
Fitting-style operator, xxvi, 152, 164167, 213-219
Fixed point, 5
least, 5, 30, 209
least post-, 6
least pre-, 6
post-, 5
pre-, 5
Fixed point of a multivalued mapping,
125
Fixed-point semantics, xxii
Fixpoint completion of a program,
xxvii, 169, 170
Formal ball, 121
Formula, 8
ground, 8
Forward Cauchy sequence, 106-108,
134
FOU R, 10, 16, 72, 167, 213-217
Four-valued interpretation, 18-20, 28
Four-valued logic, 10, 165
Four-valued valuation, 18
F P -operator, 164
Funahashi’s theorem, 187, 190
Function, 5
ω-continuous, 5, 6, 40, 42, 57, 135
antitonic, 5
continuous, 5, 68, 133, 204, 237
continuous at a point, 68, 237
contraction on a d-metric, 103
contraction on a quasimetric, 106,
107
CS-continuous, 106-111
monotonic, 5, 230
non-expanding on d-gums, 99
non-expanding on a quasimetric,
106
orbit of, 99
order continuous, 5
ordinal powers of, 5
Scott continuous, xxii, 72, 74, 170
single valued, 129, 133, 134
strictly contracting on a metric, 94
strictly contracting on a (d-)gum,
99
strictly contracting on orbits, 99
g-metric, 130-132
g-metric space, 130-132
Game, 145, 146
Gelfond–Lifschitz operator, xxvii, 34,
35, 61, 165, 171, 218, 219
Gelfond–Lifschitz transform, 34, 35,
62
Generalized ultrametric, 92, 97
Generalized ultrametric space, 97, 98
Generate-and-test, 141, 147
GL P -operator, 34
Greatest element, 2, 126
Greatest limit of a net, 75
Greatest lower bound, 2
Ground atom, 8
Ground formula, 8
267
Egli–Milner ordering, 126
Embedding of well-ordered sets, 230
Even, 25, 27, 140
Even2, 197
Eventually, 237
Eventually increasing orbit, 127
Excluded values, 213
ExistsEven, 141
Fact, 24
False, 9, 20, 161
Family of networks computes I, 212
Finer topology, 234
Finite element, 3
Finite valuation, 13
Finitely determined conjunction, 215
Finitely determined disjunction, 167,
215
Finitely determined operation, 213
First infinite ordinal, 233
First-order language, 9
Fitting model, 39-44, 55, 63, 139, 151,
174
Fitting operator, 37, 42, 43, 75, 151,
152, 161, 174
Fitting semantics, 37, 42, 55, 56, 150,
156
Fitting-style operator, xxvi, 152, 164167, 213-219
Fixed point, 5
least, 5, 30, 209
least post-, 6
least pre-, 6
post-, 5
pre-, 5
Fixed point of a multivalued mapping,
125
Fixed-point semantics, xxii
Fixpoint completion of a program,
xxvii, 169, 170
Formal ball, 121
Formula, 8
ground, 8
Forward Cauchy sequence, 106-108,
134
FOU R, 10, 16, 72, 167, 213-217
Four-valued interpretation, 18-20, 28
Four-valued logic, 10, 165
Four-valued valuation, 18
F P -operator, 164
Funahashi’s theorem, 187, 190
Function, 5
ω-continuous, 5, 6, 40, 42, 57, 135
antitonic, 5
continuous, 5, 68, 133, 204, 237
continuous at a point, 68, 237
contraction on a d-metric, 103
contraction on a quasimetric, 106,
107
CS-continuous, 106-111
monotonic, 5, 230
non-expanding on d-gums, 99
non-expanding on a quasimetric,
106
orbit of, 99
order continuous, 5
ordinal powers of, 5
Scott continuous, xxii, 72, 74, 170
single valued, 129, 133, 134
strictly contracting on a metric, 94
strictly contracting on a (d-)gum,
99
strictly contracting on orbits, 99
g-metric, 130-132
g-metric space, 130-132
Game, 145, 146
Gelfond–Lifschitz operator, xxvii, 34,
35, 61, 165, 171, 218, 219
Gelfond–Lifschitz transform, 34, 35,
62
Generalized ultrametric, 92, 97
Generalized ultrametric space, 97, 98
Generate-and-test, 141, 147
GL P -operator, 34
Greatest element, 2, 126
Greatest limit of a net, 75
Greatest lower bound, 2
Ground atom, 8
Ground formula, 8