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pr.chance – Constructing representations of chance revision capabilities

Let $P$ breathe a chance distribution over a finite Boolean algebra $mathfrak{B}$, and pickle a parameter $t_{P} in (frac{2}{3}, 1)$. Define the `revision duty of $P$‘, $R_{P}: mathfrak{B}setminus{bot} rightarrow mathbb{P}(mathfrak{B})$ as follows, (assuming that $P$ assigns constructive chance to all occasions aside from the null incident $bot$)

$R_{P}(X) = {Y in mathfrak{B}|P(Y|X) geq t}$

In phrases, the revision duty of $P$ takes an incident $X$ in $mathfrak{B}$ and returns the clique of all occasions whose conditional chance given $X$ (in line with $P$) is not less than $t_{p}$.

I wish to discover common system for setting up, for any given $P$ and any $t_{P} in (frac{2}{3}, 1)$, one other chance duty $P^{*}$ with a corresponding parameter $t_{P^{*}} in (frac{2}{3}, 1)$ such that $R_{P^{*}} = R_{P}$. In different phrases, I need a system that constructs, for any chance duty and stuck parameter within the specified meander, one other duty that (for some altenative of parameter within the specified meander) provides ascend to the identical revision duty as the unique duty.

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