I mean, you can bring up hypothetical "other logics", although it's hard to go much further than that. By definition, we can't reason about them.

On your Three Body Problem binary star world, we'd still be dealing with the same kind of energy scales, in the same universe; every mathematical theorem that's ever existed, and all known physics, would still work. What might be different, though, is which tasks the aliens find easy or hard.

When we invented computers, nobody was expecting them to be great at chess but poor at detecting if an image is of a bird. For humans, chess is hard, but seeing a bird is easy, and we assumed that was fundamental. In the 50's, the first chess algorithms were developed, and it led to the first wave of predictions the singularity was nigh. Obviously, that didn't happen.

As it turns out, ancient humans spent a lot of time looking for creatures, and evolved a lot of brain anatomy devoted to it. With chess we're starting from scratch, just like the computers. It wasn't until 2010 or so we solved the bird problem with software. Maybe your aliens are really good at chess, but blind. Or maybe, because their homeworld is unpredictable, they can learn all kinds of patterns and tasks very easily, but have no attention span and a poor memory.