Before revision: Specifically, we add structural rules of weakening and contraction for 'd propositions:Girard (1987), p.25-26, Def.1.21 and use the following logical rules : One might observe that the rules for the exponentials follow a different pattern from the rules for the other connectives, resembling the inference rules governing modalities in sequent calculus formalisations of the normal modal logic S4, and that there is no longer such a clear symmetry between the duals and .
After revision: , in which stands for a list of propositions each prefixed withSpecifically, we add structural rules of weakening and contraction for 'd propositions:Girard (1987), p.25-26, Def.1.21 and use the following logical rules : One might observe that the rules for the exponentials follow a different pattern from the rules for the other connectives, resembling the inference rules governing modalities in sequent calculus formalisations of the normal modal logic S4, and that there is no longer such a clear symmetry between the duals and .