# Founded (Auto)Epistemic Equilibrium Logic Satisfies Epistemic Splitting

## TL;DR

This paper proves that the Founded Autoepistemic Equilibrium Logic (FAEEL) satisfies the epistemic splitting property, combining it with Gelfond's original semantics and a new logic called FEEL, advancing the understanding of epistemic logic programs.

## Contribution

It demonstrates that FAEEL uniquely satisfies both foundedness and epistemic splitting, providing an alternative characterization involving G91 and FEEL.

## Key findings

- FAEEL satisfies epistemic splitting property.
- FAEEL combines G91 semantics with FEEL logic.
- Provides an alternative characterization of FAEEL.

## Abstract

In a recent line of research, two familiar concepts from logic programming semantics (unfounded sets and splitting) were extrapolated to the case of epistemic logic programs. The property of epistemic splitting provides a natural and modular way to understand programs without epistemic cycles but, surprisingly, was only fulfilled by Gelfond's original semantics (G91), among the many proposals in the literature. On the other hand, G91 may suffer from a kind of self-supported, unfounded derivations when epistemic cycles come into play. Recently, the absence of these derivations was also formalised as a property of epistemic semantics called foundedness. Moreover, a first semantics proved to satisfy foundedness was also proposed, the so-called Founded Autoepistemic Equilibrium Logic (FAEEL). In this paper, we prove that FAEEL also satisfies the epistemic splitting property something that, together with foundedness, was not fulfilled by any other approach up to date. To prove this result, we provide an alternative characterisation of FAEEL as a combination of G91 with a simpler logic we called Founded Epistemic Equilibrium Logic (FEEL), which is somehow an extrapolation of the stable model semantics to the modal logic S5. Under consideration for acceptance in TPLP.