While the computation of Craig interpolants for description logics (DLs) with the Craig Interpolation Property (CIP) is well understood, very little is known about the computation and size of interpolants for DLs without CIP or if one aims at interpolating concepts in a weaker DL than the DL of the input ontology and concepts. In this paper, we provide the first elementary algorithms computing (i) ALC-interpolants between ALC-concepts under ALCH-ontologies and (ii) ALC-interpolants between ALCQ-concepts under ALCQ-ontologies. The algorithms are based on recent decision procedures for interpolant existence. We also observe that, in contrast, uniform (possibly depth restricted) interpolants might be of non-elementary size.

翻译：尽管对于具有Craig插值性质(CIP)的描述逻辑(DL)，其Craig插值的计算已得到充分理解，但对于不具备CIP的DL，或者当目标是在比输入本体和概念更弱的DL中计算概念插值时，插值的计算与规模问题仍鲜为人知。本文首次提出了基础算法，用于计算：(i) ALCH-ontology下ALC概念间的ALC插值，以及(ii) ALCQ-ontology下ALCQ概念间的ALC插值。这些算法基于近期关于插值存在性的判定程序。同时我们观察到，与之相对，一致（可能深度受限）插值的规模可能具有非基础性。