Multi-relational data mining has become popular due to the limitations of propositional problem definition in structured domains and the tendency of storing data in relational databases. Several relational knowledge discovery systems have been developed employing various search strategies, heuristics, language pattern limitations and hypothesis evaluation criteria, in order to cope with intractably large search space and to be able to generate high-quality patterns. In this work, a new ILP-based concept discovery method is described in which user-defined specifications are relaxed. Moreover, this new method directly works on relational databases. In addition to this, a new confidence-based pruning is used in this technique. A set of experiments are conducted to test the performance of the new method.