Note that in this case, the tgd τ cannot be applied to d to produce new atoms.
But when r is applied nonrecursively to d
9
the DB r
n
(d) becomes equal to
G(y
0
,z
0
),
G(y
0
,w
0
)
To see that G(y
0
,z
0
) is in r
n
(d), note that this atom was unified with the head
of r and the instantiated body became a part of d. To see that G(y
0
,w
0
) is in
r
n
(d),
instantiate the variables of r as follows. Instantiate χ to y
0
, y to y
p
and
both ζ and w to w
0
.
The ground atoms G(y
0
,w
0
) and C(w
0
) show that (d,r
n
(d,)) does not violate
τ when the left-hand side is instantiated to G(y
0
,z
0
). Thus, r preserves τ. •
Determining
Equivalence
In this section we will show ho ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month, and much more.