I think the real question is “What does it mean to exist in a logical context?”
LO> I think Quine had it mostly right, as Thomas mentioned, because he (Quine) tried to connect the semantics to the underlying ontological referents (once again, as many have tried) by using logic and the objects quantified over. However, I don’t think that is quite right, since at least to my mind, you can quantify over notions that you don’t really think exist, ever or even potentially (and so logic is a language for describing, not a language for telling you what there is). However, logic does allow you to have access to those things, and if you quantify over them, then they are at least candidates for real things, i.e, they provide a kind of low level entry for ontological commitment. So an ontology is a logical theory, yes, but about something in the real world. The “logical theory” part of that is easier than the “real world” part.
[MW>] I take logical existence to mean the things you can talk about, which is different from do things exist in the sense of being able to kick them.