Dave Ripley: "Transitivity"

In defining "consequence relation", a number of authors insist that the relation in question be "reflexive, monotonic, and transitive". It is not so commonly noted (but it is not hard to see) that the notion of "transitivity" in play here is almost never the usual relation-theoretic notion. (This is because consequence relations almost never *are* transitive in the usual relation-theoretic sense.) In fact, there are several distinct notions that lurk under the surface of the word "transitivity" in logicians' mouths. The purpose of this talk is to try to clarify the situation: to map out a variety of properties of consequence relations we might be interested in under the name "transitivity".