A topological correctness criterion for non-commutative logic
Résumé
We formulate Girard's long trip criterion for multiplicative linear logic (MLL) in a topological way, by associating a ribbon diagram to every switching, and requiring that it is homeomorphic to the disk. Then, we extend the well-known planarity criterion for multiplicative cyclic linear logic (McyLL) to multiplicative non-commutative logic (MNL) and show that the resulting planarity criterion is equivalent to Abrusci and Ruet's original long trip criterion for MNL.
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