Translating Default Logic into Standard Auto-epistemic Logic

Abstract

Since Konolige's translation of default logic into strongly grounded autoepistemic logic (Artif. Int. 35, 1988, pp. 343-382). several other variants of Moore's original autoepistemic logic that embody default logic have been studied. All these logics differ significantly from Moore's autoepistemic logic (standard AEL) in that expansions are subject to additional groundednessconditions, Hence, the question naturalby arises whether default logic can be translated into standard AEL at all. We show that a modn] ar translation is not possible. However, we are able to construct a faithful polynomial-time translation from default logic into standard AEL, which is nonmodular. Our translation exploits the self-referentiality of AEL. It uses as an Important intermediate step an embedding of Marek's and Truszczyiiski's nonmonotonic logic N into standard AEL. It follows from our results, that the expressive power of standard AEL is strictly greater than that of default logic. © 1995, ACM. All rights reserved.