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.
FOIL now removes all positive examples covered by this new rule. If more are left then the outer loop continues.