This article presents labelled sequent calculi S{sub}(ALC) and (S{sub}(ALC)){sup}[] for the basic Description Logic (DL) ALC. Proposing Sequent Calculus (SC) for dealing with DL reasoning aims to provide a more structural way to generated explanations, from proofs as well as counter-models, in the context of Knowledge Base and Ontologies authoring tools. The ability of providing short (Polynomial) proofs is also considered as an advantage of SC-based explanations with regard to the well-known Tableaux-based reasoners. Both, S{sub}(ALC) and (S{sub}(ALC)){sup}[] satisfy cut-elimination, while (S{sub}(ALC)){sup}[] also provides ALC counter-example from unsuccessful proof-trees. Some suggestions for extracting explanations from proofs in the presented systems is also discussed.
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