Related aside: It frustrates me no end that spellcheck still doesn't appear to use any probablistic considerations, like Markov chains, to determine the intended word. And that when I click the next to last letter to make an adjustment it doesn't then change the suggestions to alternate endings, etc.. Perhaps newer devices than I have do this.
For example:
"The city councilmen refused the demonstrators a permit because they advocated violence."
Which party is "they"? There is no lexical information that can possibly answer this question. It depends entirely on an actual understanding of what "city councilmen" and "demonstrators" (in the context of city councilmen and permits!) are, and which one would be more likely to be advocating violence (and in which case that would lead to a permit denial).
Background: Until recently I worked at a symbolic AI company who was tackling this problem. I myself didn't work on this problem directly, but I became 100% convinced that their approach, while a long shot, was the only conceivable way of solving it in a fully generalized way.
I mean if us humans have a difficulty parsing each other's statements, then why should machines do any better?
It might be hard to come up with examples on the spot, but in everyday life you will routinely come across things you need to refer to by negation which are relatively uncommon.