Formal Concept Analysis and its methods for computing minimal implicational bases have been successfully applied to axiomatise minimal 𝓔𝓛-TBoxes from models, so called bases of GCIs. However, no technique for an adjustment of an existing 𝓔𝓛-TBox w.r.t. a new model is available, i.e., on a model change the complete TBox has to be recomputed. This document proposes a method for the computation of a minimal extension of a TBox w.r.t. a new model. The method is then utilised to formulate an incremental learning algorithm that requires a stream of interpretations, and an expert to guide the learning process, respectively, as input.