Ρ has two different minimal models: {A} and {B}. •
Several results concerning positive programs depend critically on the properties
(a),
(b), and (c). Fortunately, a very important property remains true.
LEMMA
2
Let Ρ be a program. Then / is a model of Ρ iff T
P
(I) C I.
Proof:
Essentially the same as the proof for programs without negation; see
Lloyd [1984]. •
This simple fact saves the whole approach based on the analysis of the
operator T
p
\ Further, the notion of a supported model can also be naturally ex-
pressed in terms of the operator T
p
. We have the following simple result.
LEMMA
3
Let Ρ be a program. The
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