Sentence Fragments

Question
In a heated debate with my classmates and teacher, we were discussing whether or not 'Balloon.' is a sentence. Don't ask how we got there, we tend to get quite off track. I decided to solve the debate I'd email you. Is this a sentence (let's say you see a balloon and state 'Balloon').  (VCE student - Billy)

Kate's response
Such a good question. There are some very complex analyses of these kinds of structures (treating them as examples of ellipsis, and reconstructing an underlying verb, for example such as "Look, balloon!"), but I never see much point in these sorts of abstract analyses (seems unhelpful to analyse something like "Exit" in terms of "Here is the exit" or "This is the exit"!). 
 
I'd simply call this a ‘sentence fragment’ or ‘clause fragment’. This would put it in the same bucket as other verbless clauses like "What a disaster!" and also verbless directives such as “Careful”!, “Two coffees”, “All aboard”! etc. (But something like your example “Balloon!” is also a little like an interjection, isn't it — so something like “Hell”! “Crumbs”! “Wow”! “Pssst”! “Shhh”! etc.). 
 
This isn't terribly satisfactory I know, given the label ‘sentence fragment’ includes a whole heap of constructions that happen to be missing crucial bits and pieces like (normally obligatory) verbs and subjects (and the bête noire of many editors and teachers!).