This seems like a very difficult problem to me. The first thing you are going to need is a dataset of examples annotated with the correct answer. If you can find a dataset with (statement, question, answer) triplets, I have some ideas of how you can use recurrent neural networks (RNNs) to proceed.

Feed your question to a RNN. Feed your answer to another RNN. Use a third RNN to produce the answer from the combined state that was built by the first two RNNs.

Here are two relevant papers by Mikolov and others:
* http://www.fit.vutbr.cz/research/groups/speech/publi/2010/mikolov_interspeech2010_IS100722.pdf
* http://www.msr-waypoint.com/pubs/176926/rnn_ctxt.pdf

If you look up "machine translation neural networks" you'll find many other things to read.

I know there are people doing something like this but using images instead of statements; the dataset is here.

https://en.wikipedia.org/wiki/Prolog
https://prolog.codeplex.com/

You are going to have a really hard time building something in Prolog that is robust enough to understand something like 'Does the dog alive?'.