Epistemic Logic Programs: A Study of Some Properties

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. 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 to change the perspective, shifting from a bottom-up to a top-down approach to splitting. Our new definition: (i) copes with concerns regarding unfoundedness of world views and subjective constraint monotonicity; (ii) is provably applicable to many of the existing semantics; (iii) operates similarly to “traditional” ASP; (iv) provably coincides 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).