SNIP
>The definition I actually work from is borrowed from Karl Popper: democracy is a form of government that may change itself non-violently. Under this defintion, which I think is pretty good, a republic can be seen as a type of democracy.

I disagree. That is a very loose definition and could also hold true for an autocracy. As long as the leader chooses his successor personally and passes control to his successor, then it is a government that changed itself nonviolently also.

I also do not believe that is an 'accepted' definition for a democracy. A more accurate definition should be created based on historical events and democratic principles derived over the years.