Here is an attempt to bring Semantic Wikis and Rules together in a different way (E1, slides 11-15):
Yet another way:

There was a SemTech2010 tutorial on Semantic MediaWiki (+ Halo extensions), which seemed to support simple inferencing:

Besides the paper you attached(*), there is also other online literature about Rule Responder :

The Intro here contains a new architecture diagram:

Here is some SemWeb background material: