  In this paper we define and study a multi-agent extension of autoepistemic
logic (AEL) called distributed autoepistemic logic (dAEL). We define the
semantics of dAEL using approximation fixpoint theory, an abstract algebraic
framework that unifies different knowledge representation formalisms by
describing their semantics as fixpoints of semantic operators. We define 2- and
3-valued semantic operators for dAEL. Using these operators, approximation
fixpoint theory allows us to define a class of semantics for dAEL, each based
on different intuitions that are well-studied in the context of AEL. We define
a mapping from dAEL to AEL and identify the conditions under which the mapping
preserves semantics, and furthermore argue that when it does not, the dAEL
semantics is more desirable than the AEL-induced semantics since dAEL manages
to contain inconsistencies.
  The development of dAEL has been motivated by an application in the domain of
access control. We explain how dAEL can be fruitfully applied to this domain
and discuss how well-suited the different semantics are for the application in
access control.
