Non-standard inferences are particularly useful in the bottom-up construction of ontologies in description logics. One of the more common non-standard reasoning tasks is the most specific concept (msc) for an ABox-individual. In this paper we present similar non-standard reasoning task: most specific concepts for models (model-mscs). We show that, although they look similar to ABox-mscs their computational behaviour can be different. We present constructions for model-mscs in FL₀ and FLE with cyclic TBoxes and for ALC∪∗ with acyclic TBoxes. Since subsumption in FLE with cyclic TBoxes has not been examined previously, we present a characterization of subsumption and give a construction for the least common subsumer in this setting
