Inductive vs. Analytical Learning

In inductive learning the learner is given $H$ and $D= \{\langle x_1, f(x_1) \rangle,\ldots,\langle x_n, f(x_n)\rangle\}$, where $f(x_i)$ is the target value for instance $x_i$. Learner must pick $h \in H$ that is consistent with $D$.
In analytical learning the learner is given $H$, $D$, and a domain theory $B$. Learner must pick $h \in H$ that is consistent with both $D$, and $B$.
We say that $h$ is consistent with $B$ if \[ \neg (B \rightarrow \neg h) \]