I'm looking for references on applications of logic (e.g. intuitionistic logic, toposes) to physics (especially quantum physics, as this is the area that I'm aware can be helped by logical considerations, but I'm open to other areas as well).
My motivation is that I read/heard multiple times that quantum physics could be well apprehended through, say, topos theory (I've heard the following sentence, which was probably an exageration : "The laws of quantum physics are the same laws as those of classical physics, but interpreted in a different topos"); but also I know that there's a thing called quantum logic even though I don't know much about it.
The references could be either technical ones (but if possible self-contained, or at least not requiring too much bagage in physics) or sort of vulgarized, not too technical ones (though I would want a bit more than "oh it can be applied, and it's interesting"), I don't really mind.