I want to build a bot that asks someone a few simple questions and branches based on the answer. I realize parsing meaning from the human responses will be challenging, but how do you setup the program to deal with the "state" of the conversation?
It will be a one-to-one conversation between a human and the bot.
I would suggest looking at Bayesian probabilities. Then just monitor the chat room for a period of time to create your probability tree.
If you do not require a learning bot, using AIML (http://www.aiml.net/) will most likely produce the result you want, at least with respect to the bot parsing input and answering based on it.
You would reuse or create "brains" made of XML (in the AIML-format) and parse/run them in a program (parser). There are parsers made in several different languages to choose from, and as far as I can tell the code seems to be open source in most cases.
I think you can look at the code for Kooky, and IIRC it also uses Markov Chains.
Also check out the kooky quotes, they were featured on Coding Horror not long ago and some are hilarious.
I think to start this project, it would be good to have a database with questions (organized as a tree. In every node one or more questions). These questions sould be answered with "yes " or "no".
If the bot starts to question, it can start with any question from yuor database of questions marked as a start-question. The answer is the way to the next node in the tree.
Edit: Here is a somple one written in ruby you can start with: rubyBOT
Imagine a neural network with parsing capabilities in each node or neuron. Depending on rules and parsing results, neurons fire. If certain neurons fire, you get a good idea about topic and semantic of the question and therefore can give a good answer.
Memory is done by keeping topics talked about in a session, adding to the firing for the next question, and therefore guiding the selection process of possible answers at the end.
Keep your rules and patterns in a knowledge base, but compile them into memory at start time, with a neuron per rule. You can engineer synapses using something like listeners or event functions.