  Approximation fixpoint theory (AFT) is an abstract and general algebraic
framework for studying the semantics of nonmonotonic logics. It provides a
unifying study of the semantics of different formalisms for nonmonotonic
reasoning, such as logic programming, default logic and autoepistemic logic. In
this paper, we extend AFT to dealing with non-deterministic constructs that
allow to handle indefinite information, represented e.g. by disjunctive
formulas. This is done by generalizing the main constructions and corresponding
results of AFT to non-deterministic operators, whose ranges are sets of
elements rather than single elements. The applicability and usefulness of this
generalization is illustrated in the context of disjunctive logic programming.
