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

[Joao Marcos]

Hi, Revantha!

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/

In this paper that we will present in TABLEAUX next week, in
particular, we study the complexity of proof-search procedures
associated to certain kinds of (two-dimensional) _analytic_
*Hilbert-style* systems (and we show that a large class of logical
matrices are axiomatisable using just this kind of systems).  It might
be worth a look!
https://arxiv.org/abs/2107.08349
On the same line, Vitor provides also other references in his response
to your post.

Best wishes,
Joao Marcos


> From: Revantha Ramanayake
>
> Dear colleagues,
>
> Many new results and new insights about classical and non-classical logics have been obtained using the sequent calculus, e.g. Gentzen's consistency argument; interpolation; decidability, complexity; etc.
>
> I would like to identify results and insights *about logics* that were *new*, and that were obtained using proof systems---other than the sequent calculus---that utilised some notion of analyticity / a restriction of proof space such as the subformula property. I am interested across all logics and all sorts of proof systems like hypersequent, nested, labelled, display, proof nets, deep inference based. Here I am viewing a logic as a set of formulas.
>
> I would be pleased to see your thoughts and references ! You could comment on my post at the The Proof Theory Blog (link below), reply here, or write to me directly.
>
> https://prooftheory.blog/2021/08/23/new-results-about-logics-using-proof-systems-other-than-sequent-calculus/
>
> Best wishes,
>
> Revantha Ramanayake
> <d.r.s.ramanayake at rug.nl>

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