  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.
