Understanding Christine Ladd-Franklin's Logic

In the late 19th century Christine Ladd-Franklin proposed a new logical system in the algebraic tradition championed by Boole, Jevons, Schröder, and her teacher Charles Sanders Peirce. This new logic was at the time celebrated as providing a novel and complete characterization of the valid syllogisms, although Ladd-Franklin’s work was largely forgotten until recently. Here we present a careful reconstruction of Ladd-Franklin’s work, concentrating on her characterization of the valid syllogisms, and we clear up some earlier confusions regarding how this novel logical system works.