 De Morgan wrote a series of six papers called “On the Syllogism” in the years 1846 to 1863 (reprinted in De Morgan 1966). In his efforts to generalize the syllogism, De Morgan replaced the copula “is” with a general binary relation in the second paper of the series dating from 1850. By allowing different binary relations in the two premises of a syllogism, he was led to introduce the composition of the two binary relations to express the conclusion of the syllogism. In this pursuit of generalized syllogisms he introduced various other operations on binary relations, including the converse operation, and he developed a fragment of a calculus for these operations. His main paper on this subject was the fourth in the series, called “On the syllogism, No. IV, and on the logic of relations” published in 1859 (see De Morgan 1966).