MVC:

Have you taken into consideration the difference between weak negation and strong negation?

I always begin classically where logic is concerned — I guess that means “strong” negation — we make a stronger start and get better mileage on that basis before we run into the specialized circumstances, mainly in computational and generalized semiotic settings, which force us to weaken our logic.

MVC:

It is so-called semiotic negation, which, by the way, was an aspect, for me, in so-called resolution logic (Ch. Sanders Peirce is mentioned on that one).

I took a computer science course on resolution-unification theorem provers at U. Illinois in the mid 1980s.  If that’s the same sort of resolution, it generalizes the modus ponens inference rule, all of which exemplify implicational inference.  Peirce’s logical graphs allow a degree of equational or information-preserving inference, a fact which Spencer Brown drew out and made more clear.