  Default logic can be regarded as a mechanism to represent families of belief
sets of a reasoning agent. As such, it is inherently second-order. In this
paper, we study the problem of representability of a family of theories as the
set of extensions of a default theory. We give a complete solution to the
representability by means of normal default theories. We obtain partial results
on representability by arbitrary default theories. We construct examples of
denumerable families of non-including theories that are not representable. We
also study the concept of equivalence between default theories.
