This paper presents the concept of Monotone Boolean Function Visual Analytics (MBFVA) and its application to the medical domain. The medical application is concerned with discovering breast cancer diagnostic rules (i) interactively with a radiologist, (ii) analytically with data mining algorithms, and (iii) visually. The coordinated visualization of these rules opens an opportunity to coordinate the rules, and to come up with rules that are meaningful for the expert in the field, and are confirmed with the database. This paper shows how to represent and visualize binary multivariate data in 2-D and 3-D. This representation preserves the structural relations that exist in multivariate data. It creates a new opportunity to guide the visual discovery of unknown patterns in the data. In particular, the structural representation allows us to convert a complex border between the patterns in multidimensional space into visual 2-D and 3-D forms. This decreases the information overload on the ...