# Toward Short and Structural ALC-Reasoning Explanations: A Sequent Calculus Approach

### Abstract:

This article presents labelled sequent calculi S_ALC and S_ALC^[] 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 \em SC-based explanations with regard to the well-known Tableaux-based reasoners. Both, S_ALC and S_ALC satisfy cut-elimination, while S_ALC^[] also provides ALC counter-example from unsuccessful proof-trees. Some suggestions for extracting explanations from proofs in the presented systems is also discussed. Keywords: description logics, sequent calculus, proof theory.

### BibTeX:

@inproceedings{publication-25,
author = {Rademaker, Alexandre and Haeusler, Edward Hermann},
title = {Toward Short and Structural ALC-Reasoning Explanations: A Sequent Calculus Approach},
booktitle = {Advances in Artificial Intelligence - SBIA 2008},
year = {2008},
publisher = {Springer Berlin},