Can we use logic to prove a moral proposition?

Here is an idea that occurred to me as I sought an "easy" way to explain G.E. Moore's "Naturalistic Fallacy." Unfortunately, Moore's arguments are a bit cloudy.  His arguments sum up in the phrase, "You can't get an ought from an is."  He is of course reflecting on Hume's manipulations of "ought-is."

The question is, can you use logic to prove a moral proposition? A logical proof might suggest that the moral proposition is scientifically proven or scientifically irrefutable, and therefore incontrovertible.

But compare:

Two and two is four.

Stealing is wrong.

The word is is different in the two formulations.  In the first statement, is means is equal to.  In the second formulation, is means should be, or, better, must be. They are not the same word.  

Yes, I agree that stealing is wrong, but can I use logic to prove it?

It is possible to prove an analytic proposition where is is used to present a logical relationship  (in this instance having to do with numbers); but logic is not--nor can it be--provable in a proposition about what we should or must do.

Morality is rather "proven" through upbringing, tradition, culture, and personal conviction (or personal indifference, alas).

Any questions?