No need to constrain yourself to FOL! Why not use some weird non-classical logic? ;-) Joking aside, rules engines typically use some form of defeasible reasoning, i.e., some not fully formalized non-monotonic logic, and it seems to be a pointless task to formalize everything. Still, I think that even from a practical perspective, looking at them through a formal lens can potentially help improve them, see this paper for an example:
http://www.inf.unibz.it/~calvanese/papers/calv-etal-IS-2018.....