In the search for knowledge graph embeddings that could capture ontological knowledge, geometric models of existential rules have been recently introduced. It has been shown that convex geometric regions capture the so-called quasi-chained rules. Attributed description logics (DL) have been defined to bridge the gap between DL languages and knowledge graphs, whose facts often come with various kinds of annotations that may need to be taken into account for reasoning. In particular, temporally attributed DLs are enriched by specific attributes whose semantics allows for some temporal reasoning. Considering that geometric models and (temporally) attributed DLs are promising tools designed for knowledge graphs, this paper investigates their compatibility, focusing on the attributed version of a Horn dialect of the DL-Lite family. We first adapt the definition of geometric models to attributed DLs and show that every satisfiable ontology has a convex geometric model. Our second contribution is a study of the impact of temporal attributes. We show that a temporally attributed DL may not have a convex geometric model in general but we can recover geometric satisfiability by imposing some restrictions on the use of the temporal attributes.
翻译:在寻找能够捕捉本体知识的知识图嵌入器时,最近引入了生存规则的几何模型,并显示Convex几何区域捕捉了所谓的准链式规则。定性描述逻辑(DL)被确定为缩小DL语言和知识图之间的差距,其事实往往带有各种说明,可能需要在推理中予以考虑。特别是,时间归属DL由特定属性丰富,其语义学允许某种时间推理。考虑到几何模型和(暂时)分辨的DL是设计用于知识图的有希望的工具,本文调查了它们的兼容性,重点是DL-Lite家族的合恩方方言的配方言。我们首先将几何体模型的定义调整为DLs,并表明每个可坐态的Otlog学都有一个Convex几何模型。我们的第二个贡献是研究时间属性的影响。我们显示,按时间归属的DL可能没有一般的等分数度模型,但我们可以通过测量时空性来恢复某些测量性限制。