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cousin_it comments on Ingredients of Timeless Decision Theory - Less Wrong
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I was thinking of some case where the cycle contains both physical and logical arrows. Logical arrows can point backwards in time, so this doesn't seem to be impossible in principle. Sorry, can't give a specific example because I don't fully understand what you mean by "logical uncertainty".
My reading is that logical nodes can point to physical nodes, but not vice versa. (Also that it doesn't make sense to say an arrow from a logical node "points backwards in time". Logical nodes are timeless.)