Relationships between the axiomatic systems of modal propositional logic

I made a diagram of this, based on Sider’s Logic for philosophy. An orange arrow from sytems S to system S’ means anything that is provable (and hence valid) in S is provable (and valid) in S’. I don’t add lables to the orange arrows since their meanings are clear. A green arrow from axiom schema to another says that the second schema is provable from the first in a particular system which I label.

Written on December 26, 2017