I wouldn't argue with the point that humans use rigorous logic and overt rules-based behavior much less than they imagine (your summary is very much a summary of the other-NLP model of mind, which I know).
I'd argue that while "refined" logic, systematic logic, might be rare, fairly crude logic, more or less indistinguishable from simply using language, is everywhere and it an incredibly powerful tool that human have. Again, being able to correct object recognition based on things people tell you is an incredibly powerful thing. You don't need a lot of full rationality for this but it gets you a lot. And that's just a small-ish example.
AGI that is as smart as say a rat would easily qualify as AGI even without language skills.
Being able to implement all the things human are good at, however, should be able to get us everything that we could do, because anything we could create, it could create too.
AGI that is as smart as say a rat would easily qualify as AGI even without language skills.
Indeed, but while a full language-using AI is ways a way at least, using language is one thing that's at sort-of describable/comprehensible as a goal. A rat is a lot more robust than any human made robot but how? Overall, I keep hearing these "there's intelligence that's totally unlike what we conceive" argument but it seems like computer programs as they exist now either do what a human could do rationally and more quickly (a conventional program) or heuristic duplicate human surface behavior (neural nets). You could sort-of argue for more but it's a bit tenuous. Human behavior is very flexible already (that's the point, right). And assuming AI is hard to create, creating something who properties we to-some-extent understand is more like than creating the wild unknown AI.
Also, "Getting to rat level" might not be the useful path to AGI. If we simply created a rat like thing, we might win the prize of "real AGI" but it would be far less useful than something we could tell what to do the way we tell humans what to do.
I, personally, just know I don't use logical rules very often at all. Usually I apply them retroactively as a post-hoc justification, or narrative, to explain a sense of discomfort or internal conflict or dissonance, but I have no way of knowing if my rationale is true other than how it makes me feel - I'm simply relying on the same mechanism, with an extra set of pattern recognition learned specifically to identify fallacies and incorrect logical constructs. If I didn't have that extra training, my explanations could be illogical and I'd be none the wiser.
I think humans are very bad at logical reasoning and very inefficient at it. Only a small % of the population ever does it and they usually do it incorrectly with biases, constructively to justify an already held conclusion. They're great at pattern recognition though. I don't think logical reasoning is anywhere on the critical path to human level AGI at a deep level. It could very well be a parallel system though to help train recognition if we don't figure out better ways of doing that.