
Shepherdson
T^(I) = Tp(I) U I and is more appropriate than T
p
when that is nonmonotonic.)
The other definition starts by defining M(Pj) as the intersection of all Herbrand
models of P
p
then M(P) as the intersection of all Herbrand models of P
2
whose
intersection with the Herbrand base of Pj is M(Pj), then M(P
n
) as the inter-
section of all Herbrand models of P
n
whose intersection with the Herbrand base
of P
n
_ j is M(P
n
_ j). Finally define M
p
= M(P
n
). For the program above, this
model is {q}, which does seem to be better in accordance with default reason-
ing than the other minimal model of comp(P), namely {p}. There is no reason
to suppose