In logic, what determines if a proposition is negative or affirmative/positive? I've heard about this concept, and it is related to negation, and LEM. However, not every negation is a negative proposition, and not every non-negated proposition is a positive/affirmative proposition. Apparently, propositional negativity and positivity can be hidden by formulation. Currently, I don't see how these properties exist outside of formulation though. To me, they have always been contingent on formulation; I don't see how something can be fundamentally negative/positive.
So, what is the conceptualization of "fundamental negativity/positivity" in logic, and how do they differ from logic to logic (if at all)?
In the section titled Irrationality of $\sqrt 2$ in this article, Andrej Bauer calls the equality and inequality of equally "positive" relations. This is the only source I can think of for how I've even encountered this concept.
 A: In that article, the topic under discussion is intuitionistic logic, which (to dramatically oversimplify) is a variant of classical logic where double negation does not bring us back to the original statement. In classical logic, we use double negation all the time in our proofs, but that article is discussing how to operate in intuitionistic logic without double negations.
In that context, I believe the author is using "positive" to describe statements where the classical statement/proof avoids double negation, so that it's equally valid in intuitionistic logic, and "negative" to describe statements that incorporate double negation, so that intuitionistic logic must treat it differently than classical logic.
This is probably a pretty sloppy explanation of something I don't understand very well; but I wanted to make a stab at describing the meaning, to emphasize that "positive" and "negative" are definitely not being used to signify true or false statements—it's a completely separate aspect of statements than true/false.
