
164
Van
Gelder
and the facts about b and g:
M
1,2) £(2,3)
*(2,1) £(3,2)
M3,4)
*(4,3)
By considering only tight NF-trees, the looping problem disappears, and
atoms like p(l,3) and p(2,3) can be put into FS
4
. For example, p(l,3) can
reduce to b(l,2) andp(2,3), but thenp(2,3) cannot reduce to b(2,l) andp(l,3)
because tightness is violated. The tight tree semantics with this program will
therefore compute the more expected result that SS also includes
{e(2,3),
e(3,2), a(2,2), a(2,3), a(3,2), a(3,3)}.
EXAMPLE 6
Recall that P
4
in Example 4 is the program with rules
p(X)^a(X),
c(X).
p(X)^
^a(X),d(X).
a(X)+b(X).
b(X)*-a(X).
together with the facts