Epistemic Logic Programs: a study of some properties

TL;DR

This paper explores properties of Epistemic Logic Programs, proposing a top-down splitting approach that aligns with traditional ASP methods and is compatible with existing semantics, enhancing modular reasoning.

Contribution

It introduces a top-down splitting approach for ELPs, proving its equivalence to the bottom-up method and its applicability across various semantics, improving modularity and methodology.

Findings

Proposed a top-down splitting approach for ELPs.

Proved equivalence of top-down and bottom-up approaches.

Enhanced compatibility with existing semantics and ASP methodology.

Abstract

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.