Is there any meaningful distinction between filtered evidence and lying? I know that in toy models these can be quite different, but in the expansive setting here, where the speaker can select the most misleading technically true fact, is there any major difference?
And how would the results here look if we expended it to allow the speaker to lie?
Here’s one way to extend a result like this to lying. Rather than assume honesty, we could assume observations carry sufficiently much information about the truth. This is like saying that sensory perception may be fooled, but in the long run, bears a strong enough connection to reality for us to infer a great deal. Something like this should imply the same computational difficulties.
I’m not sure exactly how this assumption should be spelled out, though.