Optimal Interpolation in ALC Stefan Schlobach Abstract: We describe ongoing research to support the construction of terminologies with Description Logics. Both in explanation of subsumption and in learning of terminologies we search for particular concepts because of their syntactic and semantic properties. More precisely, the set of explanations for a subsumption is the set of optimal interpolants for the two concepts, and similarly for the learning application. We provide definitions for optimal interpolation and an algorithm based on Boolean minimisation of concept-names in a tableau proof for ALC satisfiability.