A topological correctness criterion for non-commutative logic

Paul-André Melliès (1)

1 PPS - Preuves, Programmes et Systèmes

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.

Mots clés: logique linéaire; logique cyclique; logique non commutative; critère de correction; planarité; rubans

Domaines: Logique en informatique [cs.LO]

Paul-André Melliès. A topological correctness criterion for non-commutative logic. Thomas Ehrhard and Jean-Yves Girard and Paul Ruet and Philip Scott. Linear Logic in Computer Science, Cambridge University Press, pp.283-323, 2004, London Mathematical Society, Lecture Note Series 316. ⟨hal-00154204⟩