FOIL Example

Say we are tying to predict the Target-predicate GrandDaughter(x,y).
FOIL begins with
NewRule = GrandDaughter(x,y) ←
To specialize it, generate these candidate additions to the preconditions:
Equal(x,y), Female(x), Female(y), Father(x,y), Father(y.x), Father(x,z), Father(z,x), Father(y,z), Father(z,y)
and their negations.
FOIL might greedily select Father(x,y) as most promising, then
NewRule = GrandDaughter(x,y) ← Father(y,z).
Foil now considers all the literals from the previous step as well as:
Female(z), Equal(z,x), Equal(z,y), Father(z,w), Father(w,z)
and their negations.
Foil might select Father(z,x), and on the next step Female(y) leading to
NewRule = GrandDaughter (x,y) ← Father(y,z) ∧ Father(z,x) ∧ Female(y)
If this covers only positive examples it terminates the search for further specialization.