The theory and practice of coupling formal concept analysis to relational databases

In Formal Concept Analysis, a many-valued context is a collection of objects described by attributes that take on more than binary values, such as age (as integers or ranges of integer values) or color (a list or even a hierarchy of color combinations). Conceptual scaling is the process by which such a many-valued context is transformed into a formal context, by associating a concept lattice with the many-valued context. A many-valued context can be compared to a single table in a relational database populated with multiple rows and non-binary values. A generalization of conceptual scaling as a relational database as a whole should take into account the relations between objects, as expressed by means of foreign keys. Previous approaches to scaling a relational database (e.g. relational scaling) take such relations into account, but either do not maintain a separation between objects and values, which is characteristic for the unary case, or result in unary contexts only. In the approach presented in this paper, the use of n-ary scales is suggested, whereby a relational database is transformed into a family of n-ary contexts (a so called power context family). This paper describes the fundamentals of a Web application that allows connection to a relational database, its scaling interactively into a power context family, and navigation within that context family.