We identify a subclass of labelled sequents called “labelled tree sequents” and show that
these are notational variants of tree-hypersequents in the sense that a sequent of one type
can be represented naturally as a sequent of the other type. This relationship can be
extended to nested (deep) sequents using the relationship between tree-hypersequents and
nested (deep) sequents, which we also show. We apply this result to transfer proof-theoretic
results such as syntactic cutadmissibility between the tree-hypersequent calculus CSGL and …

reposiTUm: Labelled tree sequents, tree hypersequents and nested (deep) sequents …
Labelled tree sequents, tree hypersequents and nested (deep) sequents …