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：格点是用于表示和分析关系和本体知识的常用结构。特别是，对这些信息的分析需要将一个大型和高维的格点分解为一组可以理解的部分。本文提出/序模体/作为分析单位的含义。我们通过来自形式概念分析领域的（完整）标度度量来研究这些序数子结构（或标准尺度）。我们表明，底层决策问题是NP完全的，并提供有关如何逐渐识别序模体以节省计算工作量的结果。除了我们的理论结果，我们还演示了如何利用序模体从中等规模的序列数据集中检索基本含义。