We study complete approximations of an ontology formulated in a non-Horn description logic (DL) such as $\mathcal{ALC}$ in a Horn DL such as~$\mathcal{EL}$. We provide concrete approximation schemes that are necessarily infinite and observe that in the $\mathcal{ELU}$-to-$\mathcal{EL}$ case finite approximations tend to exist in practice and are guaranteed to exist when the original ontology is acyclic. In contrast, neither of this is the case for $\mathcal{ELU}_\bot$-to-$\mathcal{EL}_\bot$ and for $\mathcal{ALC}$-to-$\mathcal{EL}_\bot$ approximations. We also define a notion of approximation tailored towards ontology-mediated querying, connect it to subsumption-based approximations, and identify a case where finite approximations are guaranteed to exist.

中文翻译：

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本体近似之旅：从无号角到号角

我们研究了在非 Horn 描述逻辑 (DL) 中制定的本体的完整近似，例如 Horn DL 中的 $\mathcal{ALC}$，例如~$\mathcal{EL}$。我们提供了必然无限的具体逼近方案，并观察到在 $\mathcal{ELU}$-to-$\mathcal{EL}$ 的情况下，有限逼近在实践中往往存在，并且当原始本体是非循环时保证存在. 相比之下，对于 $\mathcal{ELU}_\bot$-to-$\mathcal{EL}_\bot$ 和 $\mathcal{ALC}$-to-$\mathcal{EL }_\bot$ 近似值。我们还定义了一个为本体介导的查询量身定制的近似概念，将其连接到基于包含的近似，并确定有限近似保证存在的情况。