Or would you try to build one big graph that encompasses physical and logical facts alike, and then use Pearl's decision procedure without further modification?
I definitely want one big graph if I can get it.
Wait, isn't it decision-computation C—rather than simulation D—whose “effect” (in the sense of logical consequence) on E we're concerned about here?
Sorry, yes, C.
Even with the node structure you suggest, we can still infer E from C and from the physical node that matches (D xor E)—unless the new rule prohibits relying on that physical node, which I guess is the idea. But what exactly is the prohibition? Are we forbidden to infer any mathematical fact from any physical indicator of that fact?
No, but whenever we see a physical fact F that depends on a decision C/D we're still in the process of making plus Something Else (E), then we express our uncertainty in the form of a causal graph with directed arrows from C to D, D to F, and E to F. Thus when we compute a counterfactual on C, we find that F changes, but E does not.
No, but whenever we see a physical fact F that depends on a decision C/D we're still in the process of making plus Something Else (E),
Wait, F depends on decision computation C in what sense of “depends on”? It can't quite be the originally defined sense (quoted from your email near the top of the OP), since that defines dependency between Platonic computations, not between a Platonic computation and a physical fact. Do you mean that D depends on C in the original sense, and F in turn depends on D (and on E) in a different sense?
...then we express our un
According to Ingredients of Timeless Decision Theory, when you set up a factored causal graph for TDT, "You treat your choice as determining the result of the logical computation, and hence all instantiations of that computation, and all instantiations of other computations dependent on that logical computation", where "the logical computation" refers to the TDT-prescribed argmax computation (call it C) that takes all your observations of the world (from which you can construct the factored causal graph) as input, and outputs an action in the present situation.
I asked Eliezer to clarify what it means for another logical computation D to be either the same as C, or "dependent on" C, for purposes of the TDT algorithm. Eliezer answered:
I replied as follows (which Eliezer suggested I post here).
If that's what TDT means by the logical dependency between Platonic computations, then TDT may have a serious flaw.
Consider the following version of the transparent-boxes scenario. The predictor has an infallible simulator D that predicts whether I one-box here [EDIT: if I see $1M]. The predictor also has a module E that computes whether the ith digit of pi is zero, for some ridiculously large value of i that the predictor randomly selects. I'll be told the value of i, but the best I can do is assign an a priori probability of .1 that the specified digit is zero.