Lattices and their order diagrams are an essential tool for communicating knowledge and insights about data. This is in particular true when applying Formal Concept Analysis. Such representations, however, are difficult to comprehend by untrained users and in general in cases where lattices are large. We tackle this problem by automatically generating textual explanations for lattices using standard scales. Our method is based on the general notion of ordinal motifs in lattices for the special case of standard scales. We show the computational complexity of identifying a small number of standard scales that cover most of the lattice structure. For these, we provide textual explanation templates, which can be applied to any occurrence of a scale in any data domain. These templates are derived using principles from human-computer interaction and allow for a comprehensive textual explanation of lattices. We demonstrate our approach on the spices planner data set, which is a medium sized formal context comprised of fifty-six meals (objects) and thirty-seven spices (attributes). The resulting 531 formal concepts can be covered by means of about 100 standard scales.

The foundation of any formal analysis of data is the identification of unique and meaningful substructures and properties. The realm of ordinal structures, in particular lattices, is no exemption to that. The field of Formal Conceptual Analysis (FCA), which derives lattices from data tables, called formal contexts, is already very well equipped with tools and notions for identifying and analyzing important substructures. One essential tool of FCA is to provide a user a lattice diagram of meaningful size, which can be interpreted (or even explained). For obvious reasons, this approach defies any applicability to data sets as they are commonly used today, as the resulting lattices are comprised of thousands of elements. In addition, the lattice diagram itself, as the primary means of communication, presents a significant hurdle to interpretation for untrained users. Common approaches tackle the first problem by data set reductions within the data tables [10, 14] or within the resulting lattice structure [1, 2, 9, 15].