 He studied the composition of relations with each other and with class-terms, and worked out the principal laws for the resulting abstract algebraic system, ultimately showing that the linear associative algebras studied by his father (Benjamin Peirce, the Harvard mathematician) could all be defined in terms of what he called “elementary relatives”. His 1870 system, although a large advance both on Boole and on De Morgan, remains notationally awkward, and in retrospect it is clear that it needed the theory of quantification. But it was the first successful attempt to extend Boole’s system into the logic of relations.