Just a brief comment on a remark made by Ash Asudeh: 
 
"All grammars, those used in statistical parsing or otherwise, attempt 
to reject ungrammatical sentences: Nobody wants their 
grammar/parser to overgenerate. Even if the claim is true of statistical 
parsers (I don't think it is), it certainly isn't true of the LFG and HPSG 
parsers and grammars noted above." 
 
That's not quite right. There is not universal agreement to the position 
that the ability to distinguish grammatical from ungrammatical 
sentences is an important function to be able to model directly, 
whether we are looking at humans or at software. There are certainly 
various serious parsing systems whose goal is to be able to parse, as 
best they can, any linguistic material that is given to them -- and 
arguably, that is what we speakers do too. I think of Microsoft 
Research's NLPWin parser as an example of such a system. 
 
Needless to say, the disagreement about this point brings into play a 
lot of very serious questions, and I think both sides of the question I 
mentioned take reasonable positions -- but my point here is to 
emphasize that Ash Sudeh's point represents one side of an issue, 
not both sides.