My advisor used to go drinking with the Cousots'. He said Cousot becomes more scrutable with more wine. I asked my advisor if he meant Cousots' papers or Cousots' conversation; his answer was "more French".

As will I be to know that about writings about his writing.

I've learned the hard way that logic is one of the most depressing subjects.

(Exhibit 1: No single completely satisfactory form of logical negation)

You could try the OG book of modern logic, to which all 20th century tracts on logic are responses to, Hegel's Science of Logic. Though its very different from what you might expect out of a logic text.

Pedantry: (wrt all) an arbitrary counterexample would be Abramsky, Domain Theory in Logical Form (1991), which is a 20th century tract on logic, but (although they may share a common Limit between them) is also something Other than a response to Hegel.

Its difficult to tease these things out, but Hegel was the dominant philosophical force of the 19th century in the UK, so any logic immediately following that period had to deal with the immensity of his influence. True, once we get to the 90s, its not clear if the authors are entirely aware of the intellectual history and are just building off of ontologies that they have uncritically adopted as "logic," but in broad strokes it is still the case that the development of logic in the 20th century is as a direct response to Hegelian philosophy.

In other words, Nothing called so much of 20th century logic into Being as Hegelian Becoming?

There is no becoming in Hegel

I'd have to read more (or get your clarification?) to understand what you mean; pp82-106* of a translation appear to cover a fair amount of Becoming to me?

https://archive.org/details/georg-wilhelm-friedrich-hegel-sc...

* including subheads such as "Moments of Becoming" and "Sublation of Becoming".

(ok, reading pp106-108 suggests that although Becoming is not Nothing for Hegel, it is self-contradictory and hence a special kind of a non-being, a determinate being?)

EDIT: aufheben seems more transparent than "sublation"

> Das Werden ist das Verschwinden von Seyn in Nichts, und von Nichts in Seyn, ... Es widerspricht sich also in sich selbst, ... eine solche Vereinigung aber zerstört sich. Dieß Resultat ist das Verschwundenseyn, aber nicht als Nichts; ... Das Werden so Übergehen in die Einheit des Seyns und Nichts, ... ist das Daseyn.

(Becoming is the disappearance of Being in Nothing, and of Nothing in Being, ... It contradicts itself ... such a union destroys itself. This result is the disappearance, but not into Nothing ... Becoming, passing thus into the unity of Being and Nothing, ... is Existence.) ??

https://www.gutenberg.org/cache/epub/6729/pg6729-images.html...

You should start with the Phenomenology of Spirit

What do you mean?

Different logical systems use different methods of handling negation. No single system is suitable for all purposes. I'm no expert, but maybe search for information about intuitionistic and paraconsistent logic and how they handle negation.