DCMatt you got it wrong I'm afraid (and this is something that rarely happens).
The stone was set for Artemis the deceased servant, by the couple, her masters, then liberators (this is just my theory, ok?), then friends.
The ancient greek word for tomb "MNHMEIO" means reminder not tomb so this is a memento mori more than a tombstone in the modern sense and the names of the ones that have taken care of the dead are listed first.
As maybe on a memorial stele, "The city of X to it's brave firefighters" for example...