Conversation

Replying to and
Thanks, yeah, I was being vague. Kalman filters are optimal for the thing they are optimal for, and then there’s various broader classes of problems for which analogous things are provably optimal (?), and you’d like a strong result for a very broad class that isn’t done…
2
1
That is exactly correct. Under some nice conditions, a noisy signal can be used in place of a non-noisy signal and you'll still get an optimal solution. LQG is a weird but practically important special case that reduces to a simpler case.
2
1
To your larger point re: expressivity of logics, control theory can be viewed as a "hack" where we work with rare islands of tractability where probabilistic systems behave as simply as first-order predicate logic systems despite not being generally reduiable to them
1
3
In general, I think the correct logic for control theory is second order... modal logic in possible worlds. Control theory rarely works with that explicitly (I did, briefly) but implicitly, that's the assumed world
1
heh my postdoc was also robot planning and also used modal logic along with temporal interval calculus (Allen) representations. It's the obvious tool to apply when you run into certain problems. But I only got as far as "you can represent things this way"
1
I combined it with a descendant for space that was mostly developed in the 90s... RCC, region connection calculus, that did for 2d space what allen did for time. It's a useful representation for abstract spatial reasoning.
1
1
There was a result that axiomatized RCC (and I think something similar would hold for TIC) as regular hausdorff (t3) spaces. So it shares the logical properties of that. You're doing probabilistic reasoning with objects in T3.
May explain why we share similar skepticisms of rationalists... did you ever read the paper "Prolegomena for any future qualitative physics" by Sacks and Doyle? It caused a major flame war that resembles the rationalist/critics arguments. I may have mentioned it.
1
2
Show replies