Tauchain is the current state of the art among blockchain researchers and AI researchers. It's not like Bitcoin at all really because Tauchain has both a knowledge base kb and a reasoner which can reason over that knowledge base. The knowledge base takes the shape of a graph, with facts representing points on the graph, and these facts connect through deductive reasoning (rules), so that with enough facts you can have the blockchain itself figure out for example that two people are friends, or that Barack Obama is the President, or that some photograph is not of a mammal, or that some action is impossible.
So the network itself can reason against whatever content you upload to it. This is something called the semantic web and it is made possible by technology like RDF (resource description framework). A casual chain of events for example can be mapped as a directed graph where you for example can describe transactions with logic.
The lead developer of Tau speaks: