On The Relation Between Default and Autoepistemic Logic

Abstract

Default logic is a formal means of reasoning about defaults: what normally is the case, in the absence of contradicting information. Autoepistemic logic, on the other hand, is 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 two systems are different, a closer analysis shows that they share 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 logic into autoepistemic logic; default theories can thus be embedded into autoepistemic logic. We also present a more surprising result: the reverse translation is also possible, so that 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. This analysis gives an interpretive semantics to default logic, and yields insight into the nature of defaults in autoepistemic reasoning.