I’m not really familiar with it. Looking it up quickly, it looks like regular formal logic formulas with some new operator symbols, I’m not sure I’d count that as a whole new notation. The 2D structure in Gentzen’s natural deduction feels much more like it warrants being called a whole new notation.
Gentzen’s stuff is from the 1930s and looks pretty much like the type theory I know.
How about linear logic? Maybe it’s a just small extensions, comparable to modal logic, but it’s new.
I’m not really familiar with it. Looking it up quickly, it looks like regular formal logic formulas with some new operator symbols, I’m not sure I’d count that as a whole new notation. The 2D structure in Gentzen’s natural deduction feels much more like it warrants being called a whole new notation.