Rough set theory is a powerful model for imprecise information. Inductive logic programming (ILP) is a machine learning paradigm that learns from real world environments, where the information available is often imprecise. The rough setting in ILP describes the situation where the setting is imprecise and any induced logic program will not be able to distinguish between certain positive and negative examples. The gRS-ILP model (generic Rough Set Inductive Logic Programming model) provides a framework for ILP in a rough setting. The formal definitions of the gRS--ILP model and the theoretical foundation for definitive description in a rough setting are presented. Definitive description is the description of data with 100\% accuracy and is of use in the context of Knowledge Discovery from Databases. Several declarative biases and the formation of elementary sets in a restricted \mbox{gRS--ILP} model are then studied. An illustrative experiment of the definitive description of mutagenesis data using the ILP system Progol is presented.