Of course I'm not talking about the kind of project that tries to emulate the brain, but something like a chatbot powered by the community — à la wikipedia — where users can input the "inputs and answers".
I know there's something called AIML, but doesn't seem very user friendly.
I think something like OpenCyc gets closer to what you're looking for, or maybe a project like OpenWIMS. Neither of those has a "chatbot" aspect though.
That said, I have recently been toying with the idea of trying to build an "open source Watson-like" system, as a platform to learn more about natural language understanding, and some other AI topics. If you're interested, shoot me an email and I'll loop you in on that.
Short-term, I'm just working on re-implementing the "ArrowSmith" Literature Based Discovery system as an intermediate learning project. That's OSS as well, and if you'd like to take a look, have at it. https://github.com/fogbeam/arrowsmith