  It is well known that, under certain conditions, it is possible to split
logic programs under stable model semantics, i.e. to divide such a program into
a number of different "levels", such that the models of the entire program can
be constructed by incrementally constructing models for each level. Similar
results exist for other non-monotonic formalisms, such as auto-epistemic logic
and default logic. In this work, we present a general, algebraicsplitting
theory for logics with a fixpoint semantics. Together with the framework of
approximation theory, a general fixpoint theory for arbitrary operators, this
gives us a uniform and powerful way of deriving splitting results for each
logic with a fixpoint semantics. We demonstrate the usefulness of these
results, by generalizing existing results for logic programming, auto-epistemic
logic and default logic.
