I'm not sure I'm answering your question right, but here's what I think:
When I studied logical fallacies in language I came across an interesting fact: 1+1 does not necessarily have to be 2. Like in:
Ann wants to talk to the principal.
The principal is Ann's father.
That means that Ann wants to talk to her father. Does this make sense, logically?
Not always. Ann's father could be sick and someone else took over his office as principal. There is a gap between intention and outcome, which in turn affects the truth value (the sense) of a context. Just like in the case of ambiguity - a grammatically correct statement doesn't always make sense to the reader.
Among other things, logician Montague grappled with meaning / sense as a means of dealing with ambiguity / so as to disambiguate a context. I find this cutting-edge.
(Ambiguity: They saw her duck. ("duck" can be either NP or a bare infinitival complement).
However, when asked how the LT system tackles ambiguity of natural language, some experts say that the computer is programmed to ask questions whenever ambiguity is present. Still not conclusive... So, I guess one of the known challenges in language technology still remains the ambiguity of semantics.