Results about logics that were new with proof systems other than sequent calculus

[Revantha Ramanayake]

Dear Joao and Vitor,

Your construction and use of a two-dimensional analytic Hilbert calculus is precisely the type of "other than sequent calculus" new result via analyticity that I was looking for. Thank you.
 
> You might already have seen the answer written by my Master's student
> Vitor Greati at your blog:
> https://prooftheory.blog/2021/08/23/new-results-about-logics-using-proof-systems-other-than-sequent-calculus/

Dear Lew and Martin,

Similar thanks for pointing out the use of the nested sequent calculus in dealing with Tarski's relation algebra, and the possibilities via addition of the extension rule to sequent systems.

I would be happy to hear about further examples of new meta-logical results obtained via analytic proof systems extending the sequent calculus. I was not aware of too many such examples, so it's very nice to encounter these.

Best wishes,

Revantha.