What's an inferential system that is not axiomatic? You mean something kike natural deduction? Oor Hilbert style calculus? I.e. logical calculi that one seta

What's an inferential system that is not axiomatic? You mean something kike natural deduction? Oor Hilbert style calculus? I.e. logical calculi that one seta up before one sets up a theory (which "initial statements" as axioms)?