Starting from Laurent’s work on Polarized Linear Logic, we define a new polarized linear deduction system which handles recursion. This is achieved by extending the cut-rule, in such a way that iteration unrolling is achieved by cut-elimination. The proof nets counterpart of this extension is obtained by allowing oriented cycles, which had no meaning in usual polarized linear logic. We also free proof nets from additional constraints, leading up to a correctness criterion as straightforward as… CONTINUE READING