A deep inference system with a self-dual binder which is complete for linear lambda calculus

We recall that SBV, a proof system developed under the methodology of deep inference, extends multiplicative linear logic with the self-dual non-commutative logical operator Seq. We introduce SBVB that extends SBV by adding the self-dual binder Sdb on names. The system SBVB is consistent because we prove that (the analogous of) cut-elimination holds for it. Moreover, the resulting interplay between Seq and Sdb can model β-reduction of linear λ-calculus inside the cut-free subsystem BVB of SBVB. The long-term aim is to keep developing a programme whose goal is to give pure logical accounts of computational primitives under the proof-search-as-computation analogy, by means of minimal and incremental extensions of SBV.