Conversation

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.
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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
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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
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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"
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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.