In this work, we aim to leverage the insights gained from our previous research: the feature expressivity required for learning general policies or sketches is typically bounded by C3 logics, and often by C2 logics. Many constructors in description logics can be categorized within these bounds. While feature pools derived from C3 logics tend to be larger and more informative than those from C2, this additional complexity may not always be necessary and can, in fact, hinder the learning process by slowing it down. Therefore, our goal is to explore learning BNF grammars based on description logic rules that enable efficient discovery of general policies or sketches, balancing expressivity and learning efficiency.