273
Index
Supported model, xxi, 31-33
Supremum, xxiii, 2, 6, 12, 75, 128
T 0 -space, 238
T 1 -space, 238
T 2 -space, 239
see also Hausdorff space
Tail of a list, 26
Tail of a net, 237
Term assignment, 11
Term over an alphabet, 8
ground, 8
Theorem,
Banach, xxiii, 93-108, 113-116,
140-147, 166, 194
Banach multivalued, 129, 134
Funahashi, 187, 190
Kleene, xxiii, 6, 7
Kleene multivalued, 135
Knaster-Tarski, 6, 7
Knaster-Tarski multivalued, 128
Matthews, 103, 104, 114, 115, 118,
147
Prieß-Crampe and Ribenboim, 100
Prieß-Crampe and Ribenboim multivalued, 130
Rutten-Smyth, 107
Rutten-Smyth multivalued, 133
Tychonoff, 240
Well-Ordering, 231
T HREE, 9, 10, 11, 16
Three-valued interpretation, 18, 28
Three-valued logic, 9
Three-valued stable model, 170
Three-valued supported model, 40,
151
Three-valued valuation, 18
Threshold, 188
Tight orbit, 127
Top element, 2
Topological space, 234
compact, 239
subspace of, 239
Topology, 234
associated with a closure operator,
236
associated with a convergence class,
68
base for, 235
coarser, 234
discrete, 77, 78, 82, 100, 235
finer, 234
generated by a continuity space, 90
indiscrete, 235
product, 80, 82, 162, 239
relative, 239
stronger, 234
subbase for, 74, 82, 167, 235
subspace, 239
weaker, 234
Total interpretation, 19, 42
Total order on a set, 1, 19
Totally bounded quasimetric space,
106-110
Totally ordered set, 1, 98, 100, 119
T P -operator, 29
Trans-complete gum, 101
Transfinite sequence, 233
Transitive relation, 1
Translation algorithm, 193, 196
Triangle inequality, 92, 98
Trivial component, 45
True, 9, 10, 20, 161
Truth ordering, 10, 15, 16
Truth set, 10
Truth value, 9, 10
both or overdefined, 10
false, 9, 20, 161
none or underdefined, 9
true, 9, 10, 20, 161
Tweety, 25
Tweety1, 25, 27, 32, 35, 36, 38, 42
Tweety2, 36, 42, 45, 183
Tweety3, 37, 42, 45
Tweety4, 47, 61
T W O, 9, 10, 11, 15
Two-valued interpretation, xxvii, 18,
19, 28
Two-valued logic, 9, 10
Index
Supported model, xxi, 31-33
Supremum, xxiii, 2, 6, 12, 75, 128
T 0 -space, 238
T 1 -space, 238
T 2 -space, 239
see also Hausdorff space
Tail of a list, 26
Tail of a net, 237
Term assignment, 11
Term over an alphabet, 8
ground, 8
Theorem,
Banach, xxiii, 93-108, 113-116,
140-147, 166, 194
Banach multivalued, 129, 134
Funahashi, 187, 190
Kleene, xxiii, 6, 7
Kleene multivalued, 135
Knaster-Tarski, 6, 7
Knaster-Tarski multivalued, 128
Matthews, 103, 104, 114, 115, 118,
147
Prieß-Crampe and Ribenboim, 100
Prieß-Crampe and Ribenboim multivalued, 130
Rutten-Smyth, 107
Rutten-Smyth multivalued, 133
Tychonoff, 240
Well-Ordering, 231
T HREE, 9, 10, 11, 16
Three-valued interpretation, 18, 28
Three-valued logic, 9
Three-valued stable model, 170
Three-valued supported model, 40,
151
Three-valued valuation, 18
Threshold, 188
Tight orbit, 127
Top element, 2
Topological space, 234
compact, 239
subspace of, 239
Topology, 234
associated with a closure operator,
236
associated with a convergence class,
68
base for, 235
coarser, 234
discrete, 77, 78, 82, 100, 235
finer, 234
generated by a continuity space, 90
indiscrete, 235
product, 80, 82, 162, 239
relative, 239
stronger, 234
subbase for, 74, 82, 167, 235
subspace, 239
weaker, 234
Total interpretation, 19, 42
Total order on a set, 1, 19
Totally bounded quasimetric space,
106-110
Totally ordered set, 1, 98, 100, 119
T P -operator, 29
Trans-complete gum, 101
Transfinite sequence, 233
Transitive relation, 1
Translation algorithm, 193, 196
Triangle inequality, 92, 98
Trivial component, 45
True, 9, 10, 20, 161
Truth ordering, 10, 15, 16
Truth set, 10
Truth value, 9, 10
both or overdefined, 10
false, 9, 20, 161
none or underdefined, 9
true, 9, 10, 20, 161
Tweety, 25
Tweety1, 25, 27, 32, 35, 36, 38, 42
Tweety2, 36, 42, 45, 183
Tweety3, 37, 42, 45
Tweety4, 47, 61
T W O, 9, 10, 11, 15
Two-valued interpretation, xxvii, 18,
19, 28
Two-valued logic, 9, 10