And all this talk raises another question: When Smash LeDeaddwarf returns as a Zombie and you kill him again, have you murdered Zombie Smash? I would say no, you han't, don't be stupid, it's not Smash any more. BUT, without intereacting with him, say you just say him shuffling down the street, you might not realise he's a Zombie (if he's fairly fresh and well covered) and, thus, wouldn't destory (in your current mind murder) him.
This is why I'd sudjest the three tier soul system, perhaps described a little imperfectly. In this system, everything has a soul which allows it to exist (which is, I think, kind of Shintoist, but I could be all wrong), which the soul stats define. This would be the soul "possessing" any living body, or animating any undead creature. Perhaps, as sudjested Greiger, a necromancer can use the power from this level of soul to give power to collections of bones and body parts, or use magic to transfer the animator soul from simple creatures like cows and doves. Maybe to power released by sacrificing things with the second level of soul releases much more power, animating many piles of bones.
So yes, undead have a soul, but the soul has an asterix.
The next tier down is what defines the presence of self awareness. Base undead and animals lack this "moral" level, which the social stats define. The thing that seperates the two in the natural and unnatural presence of the third level, which the physical stats define.