Lattices are a commonly used structure for the representation and analysis of relational and ontological knowledge. In particular, the analysis of these requires a decomposition of a large and high-dimensional lattice into a set of understandably large parts. With the present work we propose /ordinal motifs/ as analytical units of meaning. We study these ordinal substructures (or standard scales) through (full) scale-measures of formal contexts from the field of formal concept analysis. We show that the underlying decision problems are NP-complete and provide results on how one can incrementally identify ordinal motifs to save computational effort. Accompanying our theoretical results, we demonstrate how ordinal motifs can be leveraged to retrieve basic meaning from a medium sized ordinal data set.

翻译：格是用于表示和分析关系型及本体知识的常用结构。特别地，对这些知识的分析需要将大型高维格分解为一组规模适度的可理解部件。本文提出将"序模式"作为语义分析单元。我们通过形式概念分析领域中形式背景的（完全）尺度度量来研究这些序子结构（或标准尺度）。研究表明，其底层决策问题是NP完全的，同时提供了如何增量识别序模式以节省计算开销的方法。伴随理论结果，我们展示了如何利用序模式从中等规模序数据集中提取基本语义。