Filip Železný Nada Lavrač ( Eds . ) Inductive Logic Programming

A number of recent works have been focusing on analysing the phase transition of the NP-complete ILP covering test, which have been fruitful in linking this phenomenon to plateaus during heuristic search. However, it is only a facet of the ILP complexity as it is very dependent of the search strategy. Its inherent difficulty has to be studied as a whole to design efficient learners. ILP is arguably harder than attributevalue learning, which has been formalised by Gottlob et al. who showed that the simple bounded ILP consistency problem is Σ2−complete. Some authors have predicted that a phase transition could be exhibited further up the polynomial hierarchy and we show this is the case in this problem space, where the number of positive and negative examples are order parameters. Those order parameters are the same as for the k-term DNF consistency problem studied in the context of attribute-value learning. We show that the learning cost exhibits the easy-hard-easy pattern with a lgg-based learner.