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

Ordinal Motifs in Lattices