Query answering in lattice-based description logic

Recently, the description logic LE-$\mathcal{ALC}$ was introduced for reasoning in the semantic environment of the enriched formal contexts, and a tableaux algorithm was developed for checking the consistency of ABoxes in this logic \cite{van2023non}. In this paper, we study the ontology-mediated query answering in LE-$\mathcal{ALC}$. In particular, we show that several different types of queries can be answered efficiently for LE-$\mathcal{ALC}$ knowledge bases with acyclic TBoxes using our tableaux algorithm directly or by extending it with some additional rules.