Inverted Example

Target concept is Child(u,v) s.t. the child of u is v.
We are given the single positive example ($x_i$)
Child(Bob,Sharon)
and the data is described by
Male(Bob), Female(Sharon), Father(Sharon,Bob).
We have the general background knowledge ($B$)
Parent(u,v) ← Father(u,v).
So we have:
$x_i$: Male(Bob), Female(Sharon), Father(Sharon,Bob)
$f(x_i)$: Child(Bob,Sharon)
$B$: Parent(u,v) ← Father(u,v)
What satisfies $\forall_{\langle x_{i}, f(x_i) \rangle \in D} B \wedge h \wedge x_{i} \entails f(x_{i})$?
$h_{1}$: Child(u,v) ← Father(v,u)
$h_{2}$: Child(u,v) ← Parent(v,u)
Notice that $h_1$ does not require $B$.
This process of augmenting the set of predicates, based on background knowledge, is often referred to as constructive induction.