Intuitionistic BV (Extended version)

We present the logic IBV, which is an intuitionistic version of BV, in the sense that its restriction to the MLL connectives is exactly IMLL, the intuitionistic version of MLL. For this logic we give a deep inference proof system and show cut elimination. We also show that the logic obtained from IBV by dropping the associativity of the new non-commutative seq-connective is an intuitionistic variant of the recently introduced logic NML. For this logic, called INML, we give a cut-free sequent calculus.