  We revisit the issue of connections between two leading formalisms in
nonmonotonic reasoning: autoepistemic logic and default logic. For each logic
we develop a comprehensive semantic framework based on the notion of a belief
pair. The set of all belief pairs together with the so called knowledge
ordering forms a complete lattice. For each logic, we introduce several
semantics by means of fixpoints of operators on the lattice of belief pairs.
Our results elucidate an underlying isomorphism of the respective semantic
constructions. In particular, we show that the interpretation of defaults as
modal formulas proposed by Konolige allows us to represent all semantics for
default logic in terms of the corresponding semantics for autoepistemic logic.
Thus, our results conclusively establish that default logic can indeed be
viewed as a fragment of autoepistemic logic. However, as we also demonstrate,
the semantics of Moore and Reiter are given by different operators and occupy
different locations in their corresponding families of semantics. This result
explains the source of the longstanding difficulty to formally relate these two
semantics. In the paper, we also discuss approximating skeptical reasoning with
autoepistemic and default logics and establish constructive principles behind
such approximations.
