The power of beliefs or translating default logic into standard autoepistemic logic

Abstract

Since Konolige's translation of default logic into strongly grounded autoepistemic logic, 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 groundedness-conditions. Hence, the question naturally arises whether default logic can be translated into standard AEL at all. We show, that a modular translation is not possible. However, we exhibit a a faithful polynomial-time translation from propositional default logic into standard AEL which is nonmodular. It follows that the expressive power of standard AEL is strictly greater than that of default logic. Our translation uses as important intermediate step an embedding of Marek's and Truszczyński's nonmonotonic logic N into standard AEL.