This is also the notation that is used in logic as well. The thing about it is that, while every paper can have a slightly different variant of this metalangua

This is also the notation that is used in logic as well. The thing about it is that, while every paper can have a slightly different variant of this metalanguage, all texts are supposed to contain an introduction defining exactly what this means. That's because it's common that, if you are talking about a new logic, you will have new syntax as well, or a slightly different way to make inference