We have been given the following question:
Find whether the following set is unifiable or not. If unifiable, find the most general unifier(m.g.u.).
w = {PARENTS(x, FATHER(x), MOTHER(bill)), PARENTS(bill, FATHER(bill), y)}
There are three conditions for unification of two sets:
Predicate symbol must be the same.
Number of arguments in both statements must be identical.
If two similar variables are present in the SAME expression, then unification fails.
Since all three conditions are met, we can unify the above sets.
PARENTS(x, FATHER(x), MOTHER(bill))
PARENTS(bill, FATHER(bill), y)
In the first sentence, x can be replaced with bill and MOTHER(bill) can be replaced with y to form the second sentence. Hence, the most general unifier is
m.g.u. = [x/bill,MOTHER(bill)/y]