Others have mentioned how hard natural language processing is. The actual deductions are considerably easier, at least the kind you seem to want. There is a computer language called Prolog which is specifically designed to generate valid deductions from appropriately structured data. Prolog is out of vogue in the AI community because purely deductive logic is rather sterile. Still, playing with it a little (in my case very little) will give you a feeling for how complicated human reasoning is.

On the subject of the nature of time, flies and arrows...

I haven't read the Chomsky paper, but I think he used the sentence to illustrate different types of parse trees for English. He was not (primarily) making a statement about the ambiguity of the language.

Btw, there are at least two other parsings of "Time flies like an arrow. Time could be an imperative verb, which yeilds the meanings:

Time some insects as you would time an arrow.

Time insects the way an arrow would time them.

I keep thinking there is a fifth parsing as well, but I can't remember what it is.