Finally, as many have pointed it, we haven't really come across any ontology which has formalized these notions of perdurance and endurance. I would imagine if one wanted to actually enforce a 4D view in an ontology, they'd need a second order axiom, otherwise, they could use CL's ability to quantify over explicit relations via an axiom similar too
whenever you have a relation (i.e. Rel1) you want to be restricted to the 4d view, you would state:
(forall (Rel1) (4DRel Rel1))
then you would have to have something akin to:
(forall (R ...)
(if (4Drel R)
(and (R ... t) (time t) (argument ...) )
with appropriate axioms to define what an argument is.