  The paper presents a constructive fixpoint semantics for autoepistemic logic
(AEL). This fixpoint characterizes a unique but possibly three-valued belief
set of an autoepistemic theory. It may be three-valued in the sense that for a
subclass of formulas F, the fixpoint may not specify whether F is believed or
not. The paper presents a constructive 3-valued semantics for autoepistemic
logic (AEL). We introduce a derivation operator and define the semantics as its
least fixpoint. The semantics is 3-valued in the sense that, for some formulas,
the least fixpoint does not specify whether they are believed or not. We show
that complete fixpoints of the derivation operator correspond to Moore's stable
expansions. In the case of modal representations of logic programs our least
fixpoint semantics expresses well-founded semantics or 3-valued Fitting-Kunen
semantics (depending on the embedding used). We show that, computationally, our
semantics is simpler than the semantics proposed by Moore (assuming that the
polynomial hierarchy does not collapse).
