Top-down splitting property for epistemic logic programs

In this paper we consider Epistemic Logic Programs (ELPs), which extend Answer Set Programming (ASP) with “epistemic operators”. There are several approaches to the semantics of such programs in terms of World Views, which are sets of belief sets. Recent work has proposed an analysis of the structure of ELPs in terms of a concept of “splitting”, in order to be able to modularly compute their semantics in a bottom-up fashion, analogously to ‘traditional’ ASP. The proposal is brilliant but the problem is, that few of the semantics that have been proposed so far enjoy this new “Epistemic Splitting Property”. Thus, the notion of modular computation of world views does not work for most of the cases. We analyse the possibility to change the perspective about how to exploit a splitting, shifting from a bottom-up to a top-down approach. Our new definition: (i) copes with concerns regarding, e.g. “unfoundedness” of world views and “subjective constraint monotonicity”; (ii) is applicable to many of the existing semantics; (iii) coincides with the bottom-up notion of splitting on a significant class of programs.