Toward Short and Structural $\mathcal{ALC}$-Reasoning Explanations: A Sequent Calculus Approach

Abstract

This article presents labelled sequent calculi $\mathcal{{S}_{ALC}}$ and $\mathcal{{S}^{[]}_{ALC}}$ for the basic Description Logic (DL) $\mathcal{ALC}$. 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, $\mathcal{{S}_{ALC}}$ and $\mathcal{{S}^{[]}_{ALC}}$ satisfy cut-elimination, while $\mathcal{{S}^{[]}_{ALC}}$ also provides $\mathcal{ALC}$ counter-example from unsuccessful proof-trees. Some suggestions for extracting explanations from proofs in the presented systems is also discussed.