This part begins the non basic part of the book and is built around a theme of semantics preserving morphisms. First in Chapter 11 the notion of a bisimulation is developed. This is a kind of relation between structures designed to highlight the similarities between them which, as a side product, has the required semantic preserving properties. The notion subsumes most other semantic preserving morphisms.

Building on this notion, in Chapter 12 a method of constructing smaller structures from larger structures is described. This method of filtrations has completeness and decidability consequences for the sytems to which it is applied. These are developed in Chapter 13.