  Building rules on top of ontologies is the ultimate goal of the logical layer
of the Semantic Web. To this aim an ad-hoc mark-up language for this layer is
currently under discussion. It is intended to follow the tradition of hybrid
knowledge representation and reasoning systems such as $\mathcal{AL}$-log that
integrates the description logic $\mathcal{ALC}$ and the function-free Horn
clausal language \textsc{Datalog}. In this paper we consider the problem of
automating the acquisition of these rules for the Semantic Web. We propose a
general framework for rule induction that adopts the methodological apparatus
of Inductive Logic Programming and relies on the expressive and deductive power
of $\mathcal{AL}$-log. The framework is valid whatever the scope of induction
(description vs. prediction) is. Yet, for illustrative purposes, we also
discuss an instantiation of the framework which aims at description and turns
out to be useful in Ontology Refinement.
  Keywords: Inductive Logic Programming, Hybrid Knowledge Representation and
Reasoning Systems, Ontologies, Semantic Web.
  Note: To appear in Theory and Practice of Logic Programming (TPLP)
