Hint
The predicate grandparent_of/2 could be defined as
follows:
grandparent_of(X,Y) :- parent_of(X,Z),
parent_of(Z,Y).
The predicate greatgrandparent_of/2 could be defined as
follows:
greatgrandparent_of(X,Y) :- parent_of(X,Z),
parent_of(Z,A),
parent_of(A,Y).
And the predicate greatgreatgrandparent_of/2
could be defined analogously by simply adding one more
parent_of step to the definition of
greatgrandparent/2.
However, ancestor_of/2 cannot be defined in this way,
as we don't know how many 'parents we have to go back' to find an
ancestor. Anybody who is an arbitrary number of parent
relations back is an ancestor.
So, how can we express what ancestor_of means?
Well, obviously if I am the parent of somebody, I also belong to
his ancestors. Furthermore, if I am the parent of somebody and
that somebody is an ancestor of a third person, I am also an
ancestor of this third person.