Over the years, a number of mathematical theories has been stated on how to reason in the presence of general principles, guidelines and rules of thumb, that can potentially conflict with each other. We have also seen a neat number of implementations, where these theories have formed the basis for computer software for decision support and such. One particular challenge, however, is for these systems to explain to the end user the correctness of their analysis. After all, the underlying theory is highly mathematical, and not necessarily clear to those not having a background in this kind of maths. My job is therefore to try to transform these theories into something normal people can understand. At the moment, I’m working on explanations that are based on interactive discussions between man and machine that are very similar to the kind of discussions people have with each other.