In this chapter, we formalize a subset of default logic using the Cake method.
The goal of this chapter is to do a case study showing how the Cake method can be used to model a particular type of reasoning commonly used in knowledge representation and important in many applications. This will be done by representing two basic versions of default logic:
rough default logic and rough default logic with strong prerequisites
. The main difference between the two versions that will be modeled lies in different treatment of the prerequisite of a default while determining the default’s applicability. In the former, a default can be applied if its prerequisite is believed (not contradicting known information). In the latter, we may require that the prerequisite of a default (or a part of it) has to be known, rather than believed, to make the default applicable. The possibility of using both versions substantially increases the expressive power of the resulting logic. We also show that both rough default logic and rough default logic with strong prerequisites can be naturally extended to their prioritized versions by slightly changing the voting policy mechanism used.