Yeah, enacting comes in at a higher level of interpretation than is yet considered here.
The increasing levels of interpretation here are: Set theory or other math foundations; we consider sets of queries and beliefs and players with functions between them; we add porder and monotonicity; we specify proof engines and their properties like consistency; we define utilities, decision theories, and what makes some players better than others.
(Category theory is good at keeping these separate.)
I’d start talking about “enacting” when we define a decision theory like “Make the decision such that I can prove the best lower bound on utility.”.
What do you mean by deciding on a belief state? “Decision” is defined before I establish any causation from decisions to beliefs.
Oh, I thought you meant you didn’t see why any two beliefs had an upper bound. My choice to make players monotonic comes from intuition that that’s how the math is supposed to look. I’d define Query=P(Decision) as Decision->2 as well but that plainly makes no sense so I’m looking for the true posetty definition of Query, and “logical formulas” looks good so far. Switching back and forth sounds more like you want to do multiple decisions, one after the other. There’s also a more grounded case to be made that your policy should become more certain as your knowledge does, do you see it?
Yeah, enacting comes in at a higher level of interpretation than is yet considered here. The increasing levels of interpretation here are: Set theory or other math foundations; we consider sets of queries and beliefs and players with functions between them; we add porder and monotonicity; we specify proof engines and their properties like consistency; we define utilities, decision theories, and what makes some players better than others. (Category theory is good at keeping these separate.) I’d start talking about “enacting” when we define a decision theory like “Make the decision such that I can prove the best lower bound on utility.”. What do you mean by deciding on a belief state? “Decision” is defined before I establish any causation from decisions to beliefs.
Oh, I thought you meant you didn’t see why any two beliefs had an upper bound. My choice to make players monotonic comes from intuition that that’s how the math is supposed to look. I’d define Query=P(Decision) as Decision->2 as well but that plainly makes no sense so I’m looking for the true posetty definition of Query, and “logical formulas” looks good so far. Switching back and forth sounds more like you want to do multiple decisions, one after the other. There’s also a more grounded case to be made that your policy should become more certain as your knowledge does, do you see it?