Superstructural Reversible Logic

ABSTRACT. Linear logic refines conventional logic by being a ``resource-conscious'' logic. We analyze the notion of resource maintained by linear logic proofs and argue that it only focuses on a ``spatial'' dimension omitting another important ``temporal'' dimension. We generalize (or further refine using even more structural rules) linear logic to maintain combined spatial and temporal resources. The resulting logic is reversible and thus allows a study of reversible computation from a proof-theoretic perspective.