On the Learnability of Description Logic Programms

Carin-ALN as proposed recently by Rouveirol and Ventos [2000] is an interesting new rule learning bias for ILP. By allowing description logic terms as predicates of literals in datalog rules, it extends the normal bias used in ILP as it allows the use of all quantified variables in the body of a clause, instead of the normal exist quantified variables and it has atleast and atmost restrictions to access the amount of indeterminism of relations. From a complexity point of view Carin-ALN allows to handle the difficult indeterminate relations efficiently by abstracting them into determinate aggregations. This paper describes a method which enables the embedding ofCarin-ALN rule subsumption and learning into datalog rule subsumption and learning with numerical constraints [Sebag and Rouveirol, 1996]. On the theoretical side, this allows us to transfer the learnability results known for ILP to Carin-ALN rules. On the practical side, this gives us a preprocessing method, which enables ILP systems to learn Carin-ALN rules just by transforming the data to be analyzed. We show, that this is not only a theoretical result in a first experiment: learning Carin-ALN rules with the ILP system Cilgg from the standard ILP Mesh-Design dataset. Accepted to appear in: S. Matwin, C. Sammut (ed.), Proc of the 12th Int. Conf. on Inductive Logic Programming, ILP-2002, Sydney, Australia.