There's a distinction between "constrain the AI's output with logical rules to make it more reliable" and "build logical reasoning into the AI." The current strategies are trying to do the first task and I bet it'll lead to all sorts of cool technology. I strongly doubt these techniques will extend to the actual logical reasoning. Intuitively, it feels like throwing a bunch of logical rules onto AI is begging the question - I doubt bird/mammal brains actually have these logical rules baked in, I am sure it's far more sophisticated.

A trivial theorem in logic gives an example of what I mean:

If A then B <=> If (not B) then (not A)

This is really not how humans think - I don't believe we have a "contrapositive calculator" in our brain that takes arbitrary situations in and computes a contrapositive. This contrapositive theorem is a fact of the world that humans used logical thinking to understand, and which can be applied to formal logical computations that human brains aren't necessarily good at.

Specifically, I don't think non-human animals have "logical" thinking at all, they have causal thinking, and human logic is a consequence of us having exceptionally good understanding of causality. Logic is itself a special case of causality, formalized in a "generic" fashion by human language and used as a tool to help us think through tricky cases.

The contrapositive theorem takes a bit of thought for me to unwind - "so if B is not true then of course A can't be true" - but the way contrapositives are reflected in the real world takes no thought whatsoever, even if the examples are more algebraically complicated than A->B <=> (~B)->(~A):

- if the door is working and I have a key that can unlock the door, then if I can't unlock the door either I don't have the key or the door is broken. (AvB)->C <=> (~C)->(~A ^ ~B)

- if having gas implies my car can drive, then if my car can't drive I don't have gas - or possibly I was incorrect and my car is broken. (A->B <=> (~B)->(~A)) V (~)(A->B)

These cases are obvious to us because the brain has access to much fancier causal reasoning than what we can currently express in human language. For now, human language is stuck with "If a then not b" stuff. I don't think feeding this limited human language into a computer is going to burst past these limits. We need to figure out how bird/mammal brains actually model things causally.