This is better than nothing, thanks and upvote. Now let’s begin translating this stuff. AFAICT, a “decision theory” is supposed to have two parts:

1) A blah blah verbal algorithm for translating real-world problem descriptions into a certain kind of formal structure.

2) A mathematical algorithm that accepts that formal structure and outputs a decision.

I don’t fully understand what formal structure you’re proposing (a Pearl-style causal graph with additional “logical” arrows? why would this always be acyclic?), and can’t understand the algorithm until the structure is clear enough.

If the arrows are material implications, then A → B → C → A collapses via iff to a single node. Can you give an example of cyclic logical uncertainty?

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.)

This is better than nothing, thanks and upvote. Now let’s begin translating this stuff. AFAICT, a “decision theory” is supposed to have two parts:

1) A blah blah verbal algorithm for translating real-world problem descriptions into a certain kind of formal structure.

2) A mathematical algorithm that accepts that formal structure and outputs a decision.

I don’t fully understand what formal structure you’re proposing (a Pearl-style causal graph with additional “logical” arrows? why would this always be acyclic?), and can’t understand the algorithm until the structure is clear enough.

If the arrows are material implications, then A → B → C → A collapses via iff to a single node. Can you give an example of cyclic logical uncertainty?

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.)

Physical arrows shouldn’t point to logical nodes, though… right?