| The question you're asking requires non-trivial effort to answer precisely because "emulation cone" and "rulial space" are never quite all the way defined, and the question being asked in terms of these definitions is also left a big vague. Emulation cones go by various names, but perhaps the most common is the (bounded) reflexive and transitive closure of a reduction rules of a system. Another common name is the (bounded) reachable set. Rulial spaces, by which I mean the particular ones Stephen seems interested in toward the end, are higher order term rewriting systems or higher order syntax. But actually, rulial space is used throughout the text in a much more general sense. I'd consider even very canonical results from PL theory, e.g. confluence of rewriting, to be non-trivial observations about a particular rulial space. The reason for giving (or at least very vaguely hinting at) a definition for rulial spaces and emulation cones is to talk about foliations and then expressiveness. There's some connection between foliation and bisimulation that's difficult to exactly nail down, because nailing it down requires a lot more precision about the exact sort of (emulation cones we are interested in and for which) spaces. The connection between expressiveness and complexity hierarchies is immediately obvious, I think, right? > One frustrating thing that I often find is that much of Wolfram criticism is non-specific and as it's impossible for me to bucket Wolfram I can't bucket his critics either because they tend not to provide enough detail or clarity. Oy, no good deed goes unpunished :) Look, I get why it's frustrating. But, really, there's a reason that rule #0 of technical writing is to define terms before using them. The reader can only do so much. |