Ideal Refinement of Descriptions in -Log

This paper deals with learning in $\mathcal{AL}$-log, a hybrid language that merges the function-free Horn clause language Datalog and the description logic $\mathcal{ALC}$. Our application context is descriptive data mining. We introduce $\mathcal{O}$-queries, a rule-based form of unary conjunctive queries in $\mathcal{AL}$-log, and a generality order ≽  _B for structuring spaces of $\mathcal{O}$-queries. We define a (downward) refinement operator ρ _O for ≽  _B -ordered spaces of $\mathcal{O}$-queries, prove its ideality and discuss an efficient implementation of it in the context of interest.