[dTal]

I would like the PL theory analogue of "emulation cones" and "rulial space" please :)

If these concepts don't have a single name that you can just rattle off, and that we can Google - if describing them in terms of existing theory would take serious effort - then surely identifying and naming them is a major contribution?

[naasking]

PL theory is a bit of a hobby of mine, but I don't really see an exact equivalent to what Wolfram seems to be describing. His rules are like rules in a term rewriting system, but the rules of rulial space are permitted to change so they may be more expressive, perhaps like a higher-order rewrite system.