On the Relation Between Default Theories and Autoepistemic Logic

Abstract

Default theories are a formal means of reasoning about defaults : what normally is the case, in the absence of contradicting information. Autoepistemic theories, on the other hand, are meant to describe the consequences of reasoning about ignorance: what must be true if a certain fact is not known. Although the motivation and formal character of these systems are different, a closer analysis shows that they bear a common trait, which is the indexical nature of certain elements in the theory. In this paper we compare the expressive power of the two systems. First, we give an effective translation of default theories into autoepistemic logic; default theories can thus be embedded into autoepistemic logic. A more suprising result is that the reverse translation is also possible: every set of sentences in autoepistemic logic can be effectively rewritten as a default theory. The formal equivalence of these two differing systems is thus established. Some benefits of this analysis are that it gives an interpretive semantics to default theories, and yields insight into the nature of defaults in autoepistemic reasoning.