Bridging the Gap between Horn Clausal Logic and Description Logics in Inductive Learning

This paper deals with spaces of inductive hypotheses represented with hybrid languages. We adopt script A signℒ-log, a language that combines the function-free Horn clausal language DATALOG and the description logic script A signℒscript C sign by using concept assertions as type constraints on variables. For constrained DATALOG clauses we define a relation of subsumption, called B-subsumption, inspired by Buntine's generalized subsumption. We show that B-subsumption induces a quasi-order, denoted as ≥B, over the space of constrained DATALOG clauses and provide a procedure for checking ≥B under the object identity bias.