 There are now several approaches to the proof theory for \(\mathbf{R}\). There is a sequent calculus for the negation-free fragment of the logic \(\mathbf{R}\) due to Gregory Mints (1972) and J.M. Dunn (1973) and an elegant and very general approach called “Display Logic” developed by Nuel Belnap (1982). But here I will only deal with the natural deduction system for the relevant logic \(\mathbf{R}\) due to Anderson and Belnap.