Source: Douglas R. White, in 1995. Lattice Theory and its Applications: In Celebration of Garrett Birkhoff's 80th Birthday, by K. A. Baker, Garrett Birkhoff, and Rudolf Wille. Lemgo, Germany: Heidermann Verlag.

The figure illustrates the use of a nested line diagram (concept lattice) to show the structure of avoidances, from a cross-cultural study by Douglas R. White, as drawn by Rudolf Wille, p. 5, in his "Lauditorio" to Professor Birkhoff, the American mathematician, author of Lattice Theory, which appeared in 1940, and, with Saunders Mac Lane 1997, A Survey of Modern Algebra.

The distribution of avoidances in human societies (Douglas R. White 1995) shows three fundamental dimensions: husband's affines (virilateral, starting with husband's father), wife's affines (uxorilateral, starting with wife's mother), and generalized affines (starting with wife's brother's wife and extending to opposite sex siblings). The last of the three independent dimensions of the distribution is a significant exception to the 'extensionist' theory of kinship, in which terminologies and characteristic behaviors are 'extended' from closer relatives to more distant relatives. In this case, avoidance behavior in the third dimension is extended from affines (WiBrWi) to close relatives (siblings), not the other way around.

This research was begun in 1970 and the lattice drawing in 1990. The avoidance data was the testbed data distributed with Statistical Entailment Analysis.