Principles of Inductive Reasoning on the Semantic Web: A Framework for Learning in AL-Log

The design of the logical layer of the Semantic Web, and subsequently of the mark-up language SWRL, has renewed the interest in hybrid knowledge representation and reasoning. In this paper we discuss principles of inductive reasoning for this layer. To this aim we provide a general framework for learning in AL-log, a hybrid language that integrates the description logic ALC and the function-free Horn clausal language Datalog, thus turning out to be a small yet sufficiently expressive subset of SWRL. In this framework inductive hypotheses are represented as constrained Datalog clauses, organized according to the B-subsumption relation, and evaluated against observations by applying coverage relations that depend on the representation chosen for the observations. The framework is valid whatever the scope of induction (description vs. prediction) is. Yet, for illustrative purposes, we concentrate on an instantiation of the framework which supports description.