A while back I wrote a blog on our new algorithm. http://blog.athico.com/2013/11/rip-rete-time-to-get-phreaky.html Someone asked me about the new stack based system, and how backward chaining works. I replied to them in an email, but I thought others might find it useful, so have pasted it below. It's written straight from my brain onto the page, so it' a bit raw in places.; but I hope some find it useful, regardless.