  Epistemic Logic Programs (ELPs), extend Answer Set Programming (ASP) with
epistemic operators. The semantics of such programs is provided in terms of
world views, which are sets of belief sets, i.e., syntactically, sets of sets
of atoms. Different semantic approaches propose different characterizations of
world views. Recent work has introduced semantic properties that should be met
by any semantics for ELPs, like the Epistemic Splitting Property, that, if
satisfied, allows to modularly compute world views in a bottom-up fashion,
analogously to ``traditional'' ASP. We analyze the possibility of changing the
perspective, shifting from a bottom-up to a top-down approach to splitting. We
propose a basic top-down approach, which we prove to be equivalent to the
bottom-up one. We then propose an extended approach, where our new definition:
(i) is provably applicable to many of the existing semantics; (ii) operates
similarly to ``traditional'' ASP; (iii) provably coincides under any semantics
with the bottom-up notion of splitting at least on the class of Epistemically
Stratified Programs (which are, intuitively, those where the use of epistemic
operators is stratified); (iv) better adheres to common ASP programming
methodology.
