If you get through Prolog until the DCG chapter in Learn Prolog Now! mentioned by Mr. Dimitrov above, you'll have a good beginning at getting some semantics into your system, since Prolog gives you a very simple way of maintaining a database of knowledge and belief, which can be updated through question-answering.
As regards the literature, I have one major recommendation for you: run out and buy Speech and Language Processing by Jurafsky & Martin. It is pretty much the book on NLP (the first chapter is available online); used in a frillion university courses but also very readable for the non-linguist and practically oriented, while at the same time going fairly deep into the linguistics problems. I really cannot recommend it enough. Chapters 17, 18 and 21 seem to be what you're looking for (14, 15 and 18 in the first edition); they show you simple lambda notation which translates pretty well to Prolog DCG's with features.
Oh, btw, on getting the masters in linguistics; if NL semantics is what you're into, I'd rather recommend taking all the AI-related courses you can find (although any courses on "plain" linguistic semantics, logic, logical semantics, DRT, LFG/HPSG/CCG, NL parsing, formal linguistic theory, etc. wouldn't hurt...)
Reading Chomsky's original literature is not really useful; as far as I know there are no current implementations that directly correspond to his theories, all the useful stuff of his is pretty much subsumed by other theories (and anyone who stays near linguists for any matter of time will absorb knowledge of Chomsky by osmosis).
