This paper explores how the logical difference between two ontologies can be tracked using a forgetting-based or uniform interpolation (UI)-based approach. The idea is that rather than computing all entailments of one ontology not entailed by the other ontology, which would be computationally infeasible, only the strongest entailments not entailed in the other ontology are computed. To overcome drawbacks of existing forgetting/uniform interpolation tools we introduce a new forgetting method designed for the task of computing the logical difference between different versions of large-scale ontologies. The method is sound and terminating, and can compute uniform interpolants for ALC-ontologies as large as SNOMED CT and NCIt. Our evaluation shows that the method can achieve considerably better success rates (>90%) and provides a feasible approach to computing the logical difference in large-scale ontologies, as a case study on different versions of SNOMED CT and NCIt ontologies shows.