A geometrical procedure for computing relaxation

Permutative logic is a non-commutative conservative extension of linear logic suggested by some investigations on the topology of linear proofs. In order to syntactically reflect the fundamental topological structure of orientable surfaces with boundary, permutative sequents turn out to be shaped like q-permutations. Relaxation is the relation induced on q-permutations by the two structural rules divide and merge; a decision procedure for relaxation has been already provided by stressing some standard achievements in theory of permutations. In these pages, we provide a parallel procedure in which the problem at issue is approached from the point of view afforded by geometry of 2-manifolds and solved by making specific surfaces interact.