Complete Lattice: Binary Relations
As part of set theory, relations are manipulated with the algebra of sets, including complementation. Furthermore, the two sets are considered symmetrically by introduction of the converse relation, which exchanges their places. Another operation is composition of relations. Altogether these tools form the calculus of relations, for which there are textbooks by Ernst Schröder, Clarence Lewis, and Gunther Schmidt. A deeper analysis of relations involves decomposing them into subsets called concepts, and placing them in a complete lattice.