We have isolated three important properties of standard formal systems: being canonical, and having the fmp, both of which imply the third property of being Kripke-complete. We have also seen may examples of systems with these properties. In this part we look more closely at the connection between these properties.

In each of Chapters 14 and 15 we look at a system which has the fmp but is not canonical. Both of these systems have independent interest. In Chapter 16 we consider a system which is canonical but does not have the fmp. This system is custom built to have these properties but may, in time, be found to have interest in its own right. Finally, in Chapter 17, we look at two systems, one of which has all three properties and the other having none of the properties. Furthermore, these two systems have precisely the same class of unadorned models.

Taken as a whole these four chapters hint at some of the complexities that can arise in modal logic.