Constraints on Extensions of a Default Theory

In this paper, the representability of a family of theories as the set of extensions of a default theory is studied. First, a new necessary condition is given for the representability by means of general default theories; then a sufficient one is presented. The families of theories represented by default theories are also fully characterized. Finally, the paper gives an example of denumerable families of mutually inconsistent theories that are represented by a default theory but not by normal ones.