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When considering an embedder \(F\), in universe \(U\), in response to which SADT picks policy \(\pi\), I would be tempted to apply the following coherence condition:

\[ E[F(\pi)] = E[F(DDT)] = E[U] \]

(all approximately of course)

I’m not sure if this would work though. This is definitely a necessary condition for reasonable counterfactuals, but not obviously sufficient.

A potentially useful augmentation is to use absolute expected difference: \[E[|F(\pi) - F(DDT)|] = E[|F(DDT) - U|] = 0\]

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By censoring I mean a specific technique for forcing the consistency of a possibly inconsistent set of axioms.

Suppose you have a set of deduction rules \(D\) over a language \(\ell\). You can construct a function \(f_D : P(\ell) \to P(\ell)\) that takes a set of sentences \(S\) and outputs all the sentences that can be proved in one step using \(D\) and the sentences in \(S\). You can also construct a censored \(f'_D\) by letting \(f'_D(S) = \{\phi\ |\ \phi \in f_D(S) \wedge \neg \phi \not\in S\}\).

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